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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces ordinary differential equation; algebraic curve; rational parametrization; rational general solution Vo, N.; Grasegger, G.; Winkler, F., Deciding the existence of rational general solutions for first-order algebraic odes, J. Symbolic Comput., 87, 127-139, (2018) Explicit solutions, first integrals of ordinary differential equations, Geometric methods in ordinary differential equations, Nonlinear ordinary differential equations and systems, Special algebraic curves and curves of low genus, Rational and ruled surfaces Deciding the existence of rational general solutions for first-order algebraic ODEs
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Diaz, H.: The motive of the Fano surface of lines, arXiv:1602.06403v1 (Equivariant) Chow groups and rings; motives, Rational and ruled surfaces, Fano varieties The motive of the Fano surface of lines
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces super algebraic geometry; orthosymplectic group; periplectic group; super Pfaffian; tensor invariant Deligne, P.; Lehrer, GI; Zhang, RB, The first fundamental theorem of invariant theory for the orthosymplectic super group, Adv. Math., 327, 4-24, (2018) Supervarieties, Vector and tensor algebra, theory of invariants, Noncommutative algebraic geometry The first fundamental theorem of invariant theory for the orthosymplectic super group
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces hypersurfaces; Schebert calculus; cubic hypersurfaces; cubic threefolds; cubic fourfolds; Pfaffian cubics; unirationality; rationality; Picard group; intermediate Jacobian; Albanese variety; Abel-Jacobi map; conic bundles; abelian varieties; Prym varieties; Hilbert square; varieties with vanishing Chern class; Calabi-Yau varieties; holomorphic symplectic varieties; Beauville-Bogomolov decomposition theorem Hypersurfaces and algebraic geometry, Rational and ruled surfaces, \(3\)-folds, \(4\)-folds, Calabi-Yau manifolds (algebro-geometric aspects), Jacobians, Prym varieties, Picard schemes, higher Jacobians, Rationality questions in algebraic geometry, Rational and unirational varieties On the geometry of hypersurfaces of low degrees in the projective space
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces birational algebras; Zariski central rings; ideal theory of birational extensions Associative rings of functions, subdirect products, sheaves of rings, Rational and birational maps, Extensions of associative rings by ideals, Ideals in associative algebras Algebraically birational extensions
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Clifford algebra; Dirac operator Noncommutative algebraic geometry Noncommutative geometry and the difraction one dimensional network
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Del Pezzo surface; finite field; Frobenius action Finite ground fields in algebraic geometry, Rational and ruled surfaces Del Pezzo surfaces over finite fields and their Frobenius traces
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Noncommutative symmetric systems; noncommutative symmetric functions, Azumaya algebras Zhao, W.: Noncommutative symmetric systems over associative algebras. J. pure appl. Algebra 210, No. 2, 363-382 (2007) Symmetric functions and generalizations, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Automorphisms and endomorphisms, Algebraic aspects of posets Noncommutative symmetric systems over associative algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces non-commutative algebraic geometry; non-commutative curve; non-commutative symmetric Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry, Derived categories and associative algebras A representation theoretic study of non-commutative symmetric algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebraic geometry; \(\mathbb {Z}\)-algebras; birational transformations; Sklyanin algebras Noncommutative algebraic geometry, Rational and birational maps, Birational automorphisms, Cremona group and generalizations Symmetric noncommutative birational transformations
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Kimura, Y., Multi-matrix models and noncommutative Frobenius algebras obtained from symmetric groups and Brauer algebras, Commun. Math. Phys., 337, 1, (2015) Supersymmetric field theories in quantum mechanics, Topological field theories in quantum mechanics, Brauer groups of schemes, Quasi-Frobenius rings, Random matrices (probabilistic aspects) Multi-matrix models and noncommutative Frobenius algebras obtained from symmetric groups and Brauer algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative k-algebras; deformation theory; moduli Noncommutative algebraic geometry, Fine and coarse moduli spaces, Stacks and moduli problems, Noncommutative local and semilocal rings, perfect rings Geometry of noncommutative \(k\)-algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces weakly normal extension of noetherian rings; symmetric algebra [I]Itoh S.,On weak normality and symmetric algebras. J. Algebra 85 (1983) 40--50. Extension theory of commutative rings, Commutative Noetherian rings and modules, Picard groups On weak normality and symmetric algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Zhao, W, Noncommutative symmetric functions and the inversion problem, Internat. J. Algebra Comput., 18, 869-899, (2008) Symmetric functions and generalizations, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), (Equivariant) Chow groups and rings; motives Noncommutative symmetric functions and the inversion problem
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces homogeneous spaces; symmetric spaces; Lie group; Poisson algebra Group actions on varieties or schemes (quotients), Homogeneous spaces and generalizations, Poisson algebras, Homogeneous spaces Weakly symmetric and weakly commutative spaces
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces finite Coxeter system; Dunkl elements; coinvariant algebras of Coxeter groups; multiparameter deformation; quantized bracket algebras; quantum cohomology ring; flag variety Kirillov, A., Maeno, T.: Noncommutative algebras related with Schubert calculus on Coxeter groups. Eur. J. Comb. \textbf{25}, 1301-1325 (2004). Preprint RIMS-1437, 2003 Grassmannians, Schubert varieties, flag manifolds, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Reflection and Coxeter groups (group-theoretic aspects) Noncommutative algebras related with Schubert calculus on Coxeter groups
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces derivations; free algebras; Jacobian matrices; left-symmetric algebras Lie-admissible algebras, Other \(n\)-ary compositions \((n \ge 3)\), Jacobian problem, Automorphisms, derivations, other operators (nonassociative rings and algebras), Free nonassociative algebras Left-symmetric algebras of derivations of free algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebraic geometry; simple modules Noncommutative algebraic geometry, Representations of quivers and partially ordered sets Geometry of noncommutative algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces non-commutative algebraic geometry; simple modules Noncommutative algebraic geometry, Representations of quivers and partially ordered sets Geometry of noncommutative algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative symmetric functions; shifted symmetric functions; Schur functions; quasideterminants Symmetric functions and generalizations, Classical problems, Schubert calculus Noncommutative shifted symmetric functions
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Jordan algebras; symmetric matrices; complex numbers; Chow form; reciprocal variety Idempotents, Peirce decompositions, Grassmannians, Schubert varieties, flag manifolds Jordan algebras of symmetric matrices
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative crepant resolution; superpotential algebra; square superpotential algebra; superpotential; quiver; quiver algebra; dimer model; Azumaya locus; Calabu-Yau algebra; noncommutative algebraic geometry; torusimbedding C. Beil, The geometry of noncommutative singularity resolutions, . Noncommutative algebraic geometry, Semiprime p.i. rings, rings embeddable in matrices over commutative rings, Representations of quivers and partially ordered sets On the noncommutative geometry of square superpotential algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative generalizations of polynomial algebras; coordinate algebras; noncommutative differential geometry; noncommutative algebraic geometry Dubois-Violette, M.: Noncommutative coordinate algebras. In: Blanchard, E. (ed.) Quanta of Maths, dédié à à A. Connes. In: Clay Mathematics Proceedings, pp. 171--199. Clay Mathematics Institute (2010) Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Quadratic and Koszul algebras, Ordinary and skew polynomial rings and semigroup rings, Graded rings and modules (associative rings and algebras) Noncommutative coordinate algebras.
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative affine spaces; Kapranov's formula; noncommutative holomorphic functional calculus DOI: 10.1016/j.crma.2014.10.020 Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Noncommutative algebraic geometry Noncommutative affine spaces and Lie-complete rings
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces second quantization; twisted Hopf algebra; \(*\)-deformation; field theory on Moyal spaces; quantization in field theory; cohomological methods; noncommutative geometry methods Fiore G 2010 On second quantization on noncommutative spaces with twisted symmetries \textit{J. Phys. A: Math. Theor.}43 155401 Quantization in field theory; cohomological methods, Noncommutative geometry methods in quantum field theory, Hopf algebras and their applications, Deformations of associative rings, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Deformation quantization, star products On second quantization on noncommutative spaces with twisted symmetries
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces monoidal category; Hopf module; equivariant sheaf Skoda, Z.: Some equivariant constructions in noncommutative algebraic geometry, Georgian math. J. 16, No. 1, 183-202 (2009) Noncommutative algebraic geometry Some equivariant constructions in noncommutative algebraic geometry
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces NCS systems; noncommutative symmetric functions; differential operator specialization; Hopf algebra DOI: 10.1016/j.aim.2007.03.002 Symmetric functions and generalizations, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Rings of differential operators (associative algebraic aspects), Automorphisms and endomorphisms Differential operator specializations of noncommutative symmetric functions
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces classical invariant theory; covariants; Gordan's algorithm M.~Olive and R.~Lercier. Covariant algebra of the binary nonic and the binary decimic. \textit{Submitted.}, 2016. Actions of groups on commutative rings; invariant theory, Theory of modules and ideals in commutative rings, Computational aspects in algebraic geometry Covariant algebra of the binary nonic and the binary decimic
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative quadric hypersurfaces Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Derived categories and associative algebras, Abelian categories, Grothendieck categories Algebras associated to noncommutative conics in quantum projective planes
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces stable vector bundles on curves; Brill-Noether locus E. Ballico: ''On the symmetric algebra of stable vector bundles on curves'', Quart. J. Math., Vol. 52, (2001), pp. 261--268. Vector bundles on curves and their moduli, Plane and space curves On the symmetric algebra of stable vector bundles on curves
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces finite Cohen-Macaulay representation type; graded isolated singularity; AS-Cohen-Macaulay algebras; noncommutative quadric hypersurfaces 10.1090/proc/12527 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.), Cohen-Macaulay modules in associative algebras, Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry Noncommutative graded algebras of finite Cohen-Macaulay representation type
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces commutator filtration; Poisson algebra; \(d\)-smooth algebra Cortiñas, G, The structure of smooth algebras in kapranov's framework for noncommutative geometry, J. Algebra, 281, 679-694, (2004) Noncommutative algebraic geometry, Local deformation theory, Artin approximation, etc., Rings arising from noncommutative algebraic geometry The structure of smooth algebras in Kapranov's framework for noncommutative geometry
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces vector space; symmetric algebra; direct sum; irreducible polynomial GL(V)-modules; GL(V)-invariant ideals; action; decomposition formula; Pieri formulas Daszkiewicz, A.: On the invariant ideals of the symmetric algebra \(S{\cdot}\)(V\(\oplus{\Lambda}\)2V). J. algebra 125, 444-473 (1989) Representation theory for linear algebraic groups, Group actions on varieties or schemes (quotients), Linear algebraic groups over arbitrary fields On the invariant ideals of the symmetric algebra \(S.(V\oplus \Lambda ^ 2V)\)
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces C. Brouder, N. Bizi and F. Besnard, \textit{The Standard Model as an extension of the noncommutative algebra of forms}, arXiv:1504.03890 [INSPIRE]. Noncommutative geometry in quantum theory, Noncommutative algebraic geometry, Finite-dimensional groups and algebras motivated by physics and their representations, Electromagnetic interaction; quantum electrodynamics, Other elementary particle theory in quantum theory Space and time dimensions of algebras with application to Lorentzian noncommutative geometry and quantum electrodynamics
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces classical Lie algebras; coadjoint representation; symmetric invariants Poisson algebras, Group actions on varieties or schemes (quotients), Simple, semisimple, reductive (super)algebras, Semisimple Lie groups and their representations Semi-direct products involving \(\mathrm{Sp}_{2n}\) or \(\mathrm{Spin}_n\) with free algebras of symmetric invariants
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebraic geometry; spectrum of an abelian category; localizations; canonical topologies A. L. Rosenberg, Noncommutative local algebra, Geometric and Functional Analysis 4 (1994), 545--585. Noncommutative algebraic geometry, Abelian categories, Grothendieck categories, Localization of categories, calculus of fractions Noncommutative local algebra
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric pair; nilpotent variety; complex simple Lie algebra Sekiguchi, Jirō, The nilpotent subvariety of the vector space associated to a symmetric pair, Publ. Res. Inst. Math. Sci., 20, 1, 155-212, (1984) Group actions on varieties or schemes (quotients), Nilpotent and solvable Lie groups, Complex Lie groups, group actions on complex spaces, Lie algebras of linear algebraic groups, Homogeneous spaces and generalizations The nilpotent subvariety of the vector space associated to a symmetric pair
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces invariant function algebra; antisymmetric algebra homogeneous space; Lie group; orbit Banach algebras of continuous functions, function algebras, Ideals, maximal ideals, boundaries, Group actions on affine varieties Invariant function algebras on compact commutative homogeneous spaces
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces character sheaves; irreducible characters; unipotent representations; complex reductive groups; connected complex reductive Lie group; differential operators; D(X)-modules; symmetric variety Ginsburg, V. : Admissible modules on a symmetric space , Astérisque 173-174 (1989) 199-255. General properties and structure of complex Lie groups, Complex Lie groups, group actions on complex spaces, Group actions on varieties or schemes (quotients), Representation theory for linear algebraic groups, Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.), Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Sheaves of differential operators and their modules, \(D\)-modules Admissible modules on a symmetric space
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Schedler, T., Deformations of algebras in noncommutative geometry, (Noncommutative Algebraic Geometry, Math. Sc. Research Institute Pub., vol. 64, (2016), Cambridge University Press) Formal methods and deformations in algebraic geometry, Deformations of associative rings, Noncommutative algebraic geometry, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Differential graded algebras and applications (associative algebraic aspects), Filtered associative rings; filtrational and graded techniques Deformations of algebras in noncommutative geometry
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Umirbaev U. U., Associative, Lie, and left-symmetric algebras of derivations 21 (3) pp 851-- (2016) Lie-admissible algebras, Exceptional (super)algebras, Lie algebras of vector fields and related (super) algebras, Jacobian problem, Connections of Hopf algebras with combinatorics Associative, Lie, and left-symmetric algebras of derivations
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces net of \(C^\ast\)-algebras; presheaf; duality; gerbe Vasselli, E., Presheaves of symmetric tensor categories and nets of C*-algebras, J. Noncommut. Geometry, 9, 121-159, (2015) General theory of \(C^*\)-algebras, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Differential geometric aspects of gerbes and differential characters Presheaves of symmetric tensor categories and nets of \(C^\ast\)-algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces semisimple modules; Jacobson radical; central simple algebras; Brauer group; primitive rings; density theorem; representations of finite groups; global dimension; textbook Farb, B.; Dennis, R. K.: ''Noncommutative algebra,'', graduate texts in mathematics. (1993) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras, Finite-dimensional division rings, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general, Simple and semisimple modules, primitive rings and ideals in associative algebras, Group rings of finite groups and their modules (group-theoretic aspects), Jacobson radical, quasimultiplication, General module theory in associative algebras, Brauer groups of schemes Noncommutative algebra
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces generic matrix; determinantal ideals; Cohen-Macaulay normal domain; divisor class group; symmetric algebra W. Bruns andA. Simis, Symmetric algebras of modules arising from a fixed submatrix of ageneric matrix. J. Pure. Appl. Algebra49, 227-245 (1987). Other special types of modules and ideals in commutative rings, Ideals and multiplicative ideal theory in commutative rings, Determinantal varieties, Polynomial rings and ideals; rings of integer-valued polynomials Symmetric algebras of modules arising from a fixed submatrix of a generic matrix
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces flat localizations of Abelian categories; structure presheaves of modules; quantized algebras; noncommutative schemes in categories; left spectrum; maximal left ideals; completely prime left ideals; categories of rings; Levitzki radical; quasi-affine schemes; projective spectra; quantized rings; quantum planes; algebra of \(q\)-differential operators; Weyl algebras; quantum envelopes; coordinate rings; generalized Weyl algebras; skew polynomial rings; Serre subcategories; Grothendieck categories; hyperbolic rings; skew PBW monads; monoidal category; Kac-Moody and Virasoro Lie algebras; semigroup-graded monads; Gabriel-Krull dimension Rosenberg, A.L.: Algebraic Geometry Representations of Quantized Algebras. Kluwer Academic Publishers, Dordrecht, Boston London (1995) Research exposition (monographs, survey articles) pertaining to associative rings and algebras, Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras, Quantum groups (quantized enveloping algebras) and related deformations, Noncommutative algebraic geometry, Torsion theories; radicals on module categories (associative algebraic aspects), Rings of differential operators (associative algebraic aspects), Local categories and functors, Abelian categories, Grothendieck categories, Graded rings and modules (associative rings and algebras), Associative rings of functions, subdirect products, sheaves of rings, ``Super'' (or ``skew'') structure, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Abstract manifolds and fiber bundles (category-theoretic aspects) Noncommutative algebraic geometry and representations of quantized algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Koszul Clabi-Yau algebra; Koszul dual algebra; Koszul coalgebra; Batalin-Vilkoviski algebra; \(n\)-Calabi-Yau algebra; Hochschild cohomology; Hochschild cohomology; Gerstenhaber bracket X. Chen, S. Yang and G. D. Zhou, Batalin--Vilkovisky algebras and the non-commutative Poincaré duality of Koszul Calabi--Yau algebras, J. Pure Appl. Algebra, 220 (2016), no. 7, 2500--2532. Zbl 06546716 MR 3457981 Noncommutative algebraic geometry, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Rings arising from noncommutative algebraic geometry, Duality in applied homological algebra and category theory (aspects of algebraic topology) Batalin-Vilkovisky algebras and the noncommutative Poincaré duality of Koszul Calabi-Yau algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces bi-graded structures; duality; elimination theory; generalized zero of a matrix; generator degrees; Hilbert-Burch matrix; infinitely near singularities; Koszul complex; local cohomology; linkage; matrices of linear forms; Morley forms; parametrization; rational plane curve; rational plane sextic; Rees algebra; Sylvester form; symmetric algebra 10.1016/j.jalgebra.2016.08.014 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Plane and space curves, Singularities of curves, local rings, Rational and birational maps The bi-graded structure of symmetric algebras with applications to Rees rings
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces representation theory; noncommutative deformation theory Formal methods and deformations in algebraic geometry, Noncommutative algebraic geometry The algebra of observables in noncommutative deformation theory
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative regular domain; joint invariant subspaces; Beurling-Lax-Halmos-type representation; wandering subspaces; characteristic functions; universal model Invariant subspaces of linear operators, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones), Canonical models for contractions and nonselfadjoint linear operators, Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc., Noncommutative algebraic geometry Invariant subspaces and operator model theory on noncommutative varieties
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric semisimple Lie algebras; S-triples; polarizations Patrice Tauvel, Quelques résultats sur les algèbres de Lie symétriques, Bull. Sci. Math. 125 (2001), no. 8, 641 -- 665 (French, with French summary). Simple, semisimple, reductive (super)algebras, Group actions on varieties or schemes (quotients) Some results about symmetric Lie algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces cohomology ring; Yang--Baxter equation; flag variety; Grothendieck ring Kirillov, A., Maeno, T.: On some noncommutative algebras related with K-theory of flag varieties. IRMN \textbf{60}, 3753-3789. Preprint RIMS, 2005 Grassmannians, Schubert varieties, flag manifolds, Noncommutative algebraic geometry On some noncommutative algebras related to \(K\)-theory of flag varieties. I
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces singular points of a hypersurface; symmetric algebra Singularities of surfaces or higher-dimensional varieties, Polynomial rings and ideals; rings of integer-valued polynomials Singularities and symmetric algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces homogeneous space; symmetry; moment map; Lie algebra, hyper-Hermitian; connection with torsion; nearly Kähler T. B. Madsen, A. Swann, Homogeneous spaces, multi-moment maps and (2, 3)-trivial algebras, AIP Conf. Proc. 1360 (2011), 51--62. Symplectic manifolds (general theory), Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry, Homogeneous spaces and generalizations, Homology and cohomology of homogeneous spaces of Lie groups Homogeneous spaces, multi-moment maps and \((2,3)\)-trivial algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative projective geometry; noncommutative surfaces; Sklyanin algebras; noncommutative blowing up; Noetherian graded rings; sporadic ideals; divisor layering; graded quotient ring; twisted homogeneous coordinate ring; elliptic algebra; exceptional line modules; Godie torsion module D. Rogalski, S. J. Sierra and J. T. Stafford, Noncommutative blowups of elliptic algebras, Algebr. Represent. Theory, (2014), 1--39.Zbl 06445654 MR 3336351 Noncommutative algebraic geometry, Elliptic curves, Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.), Noetherian rings and modules (associative rings and algebras), Rings arising from noncommutative algebraic geometry, Graded rings and modules (associative rings and algebras) Noncommutative blowups of elliptic algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces quivers; \(\mathbb{N}Q\)-algebras; bi-symplectic structures; double Poisson algebras; noncommutative algebraic geometry Noncommutative algebraic geometry, Differential graded algebras and applications (associative algebraic aspects), Poisson manifolds; Poisson groupoids and algebroids Noncommutative bi-symplectic \(\mathbb{N}Q\)-algebras of weight 1
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces non-commutative \(C^*\)-algebras; non-commutative spaces; Connes' non-commutative geometry; spectral theory of \(C^*\)-algebras; limits of non-commutative lattices; Gel'fand-Naimark theory; vector bundles on a compact manifold; projective modules over the ring of differentiable functions; \(K\)-theory for \(C^*\)-algebras; infinitesimal with the Dixmier trace; spectral triple; Riemannian spin manifold; non-commutative differential forms; connections; gauge transformations; bosonic, fermionic and gravity models Landi, \textit{An introduction to noncommutative spaces and their geometry}, Springer, Berlin Germany (1997). Noncommutative differential geometry, Research exposition (monographs, survey articles) pertaining to functional analysis, Noncommutative algebraic geometry, \(K\)-theory and operator algebras (including cyclic theory), Quantization in field theory; cohomological methods, Applications of selfadjoint operator algebras to physics, Noncommutative topology An introduction to noncommutative spaces and their geometries
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebraic geometry; algebras satisfying a polynomial identity; quantum groups; schematic algebras; regular algebras Noncommutative algebraic geometry, Quantum groups (quantized enveloping algebras) and related deformations, Rings with polynomial identity, Rings arising from noncommutative algebraic geometry Noncommutative algebraic geometry: From pi-algebras to quantum groups
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric composition algebra; Okubo algebra; automorphism group; centralizer; idempotent Composition algebras, Group schemes, Exceptional (super)algebras, Linear algebraic groups over arbitrary fields Order 3 elements in \(G_2\) and idempotents in symmetric composition algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces left-symmetric algebras; Novikov algebras; nilpotent algebras; algebraic classification; geometric classification Lie-admissible algebras, Nonassociative algebras satisfying other identities, Fibrations, degenerations in algebraic geometry, Group actions on varieties or schemes (quotients) The algebraic and geometric classification of nilpotent left-symmetric algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces left symmetric algebras; Lie-admissible algebras; semisimple algebraic groups; algebra of invariants; representations Baues, O., Left-symmetric algebras for \(g l(n)\), \textit{Transactions of the American Mathematical Society}, 351, 7, 2979-2996, (1999) Nonassociative algebras satisfying other identities, Lie algebras of linear algebraic groups, Group actions on varieties or schemes (quotients), Lie-admissible algebras, Representation theory for linear algebraic groups Left-symmetric algebras for \(\mathfrak{gl}(n)\).
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces operad; associative algebra; unital algebra; model category; mapping space; moduli stack F. Muro, Moduli spaces of algebras over nonsymmetric operads, Algebr. Geom. Topol., 14 (2014), 1489--1539.Zbl 1305.18036 MR 3190602 Inst. Hautes ÉĽtudes Sci. Publ. Math., 117 (2013), 271--328.Zbl 1328.14027 MR 3090262 Algebraic moduli of abelian varieties, classification, Abstract and axiomatic homotopy theory in algebraic topology Moduli spaces of algebras over nonsymmetric operads
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebraic geometry; deformed preprojective algebra; McKay correspondence; Nakajima quiver variety Baranovsky, V.; Ginzburg, V.; Kuznetsov, A., Quiver varieties and a noncommutative \(\mathbb{P}^2\), Compos. Math., 134, 3, 283-318, (2002) Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry Quiver varieties and a noncommutative \(\mathbb P_2\)
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric product; equivariant formality; maximal variety; gamma product Equivariant homology and cohomology in algebraic topology, Symmetric products and cyclic products in algebraic topology, Topology of real algebraic varieties Symmetric products of equivariantly formal spaces
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces affine flag variety; canonical basis; representation; Lie algebra; noncommutative Springer resolution Bezrukavnikov, Roman; Mirković, Ivan, Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution, Annals of Mathematics, 178, 835-919, (2013) Modular Lie (super)algebras, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Classical groups (algebro-geometric aspects) Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Grothendieck category; ideal of generator; noncommutative closed subspace Noncommutative algebraic geometry A remark on closed noncommutative subspaces
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces skew-symmetric matrices; Grassmannian; secant bundle; uniform bundle; constant rank; orbits; Veronese embedding Fania, Maria Lucia; Mezzetti, Emilia, Vector spaces of skew-symmetric matrices of constant rank, Linear Algebra Appl., 434, 12, 2383-2403, (2011) Algebraic systems of matrices, Grassmannians, Schubert varieties, flag manifolds, Projective techniques in algebraic geometry, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Hermitian, skew-Hermitian, and related matrices, Vector spaces, linear dependence, rank, lineability Vector spaces of skew-symmetric matrices of constant rank
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces depth; symmetric algebra; analytic spread; reduction number; property \(G_s\); Artin-Nagata property; Cohen-Macaulay property; minimal presentation matrix Mark R. Johnson, Depth of symmetric algebras of certain ideals, Proc. Amer. Math. Soc. 129 (2001), no. 6, 1581 -- 1585. Dimension theory, depth, related commutative rings (catenary, etc.), Cohen-Macaulay modules, Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Families, moduli of curves (algebraic) Depth of symmetric algebras of certain ideals
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Noncommutative algebraic geometry, de Rham cohomology and algebraic geometry, Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Rings arising from noncommutative algebraic geometry, Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) Spectral algebras and non-commutative Hodge-to-de Rham degeneration
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces semi-simple Lie algebra; self-dual symmetric spaces V. L. Popov, AMS Transl., Ser. 2, \textbf{213}, pp. 215-222. Homogeneous spaces and generalizations, Group actions on varieties or schemes (quotients), Projective techniques in algebraic geometry, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) Self-dual projective algebraic varieties associated with symmetric spaces
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces differential graded categories; triangulated categories; derived noncommutative schemes; finite-dimensional algebras; geometric realizations; noncommutative algebraic geometry; quasi-coherent sheaves; homological algebra; perfect complexes; unbounded derived category; enough injectives; classical generator; homotopy category; enhanced category; noncommutative scheme; noncommutative derived scheme; compactification; resolution of singularities; Serre functor; geometric realization; pure geometric realization; phantoms; quasi-phantoms; Krull-Schmidt partners Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.), Noncommutative algebraic geometry, Differential graded algebras and applications (associative algebraic aspects), Derived categories, triangulated categories, Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Chain complexes (category-theoretic aspects), dg categories Derived noncommutative schemes, geometric realizations, and finite dimensional algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces translation equation; flow; rational vector fields; linear ODEs; autonomous non-linear ODEs; first order linear PDEs; algebraic functions; Lie bracket; commuting flows; Cremona groups Linear ordinary differential equations and systems, Dynamics induced by flows and semiflows, Algebraic functions and function fields in algebraic geometry, Explicit solutions, first integrals of ordinary differential equations Planar 2-homogeneous commutative rational vector fields
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces implicitization; symmetric algebra; Rees algebra Busé, Laurent; Chardin, Marc; Jouanolou, Jean-Pierre, Torsion of the symmetric algebra and implicitization, Proc. amer. math. soc., 137, 6, 1855-1865, (2009) Torsion modules and ideals in commutative rings, Local cohomology and commutative rings, Rational and birational maps, Computational aspects of algebraic surfaces Torsion of the symmetric algebra and implicitization
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces nonregular reductive prehomogeneous vector spaces DOI: 10.1006/jabr.2000.8607 Homogeneous spaces and generalizations, Prehomogeneous vector spaces Nonregular 2-simple prehomogeneous vector spaces of type I and their relative invariants
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces non-commutative motives; non-commutative algebraic geometry; non-connective algebraic K-theory; secondary K-theory; Hochschild homology; negative cyclic homology; periodic cyclic homology D.-C. Cisinski & G. Tabuada, ``Symmetric monoidal structure on non-commutative motives'', J. K-Theory9 (2012) no. 2, p. 201-268 Negative \(K\)-theory, NK and Nil, \(K\)-theory and homology; cyclic homology and cohomology, Enriched categories (over closed or monoidal categories), \(K\)-theory of schemes, Noncommutative algebraic geometry Symmetric monoidal structure on non-commutative motives
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces nonassociative algebra; torsion algebra; formal manifold; formal connection. de Rham theory in global analysis, Composition algebras, Noncommutative algebraic geometry Nonassociative algebras: a framework for differential geometry
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces hyperplane arrangement; arrangements of linear subspaces; graph curve; syzygy; equations of secant varieties Schenck, Hal; Sidman, Jessica: Commutative algebra of subspace and hyperplane arrangements, 639-665 (2013) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Enumerative problems (combinatorial problems) in algebraic geometry, Syzygies, resolutions, complexes and commutative rings Commutative algebra of subspace and hyperplane arrangements
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces easy quantum groups; quantum homogeneous space; noncommutative manifold; Weingarten integration Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Noncommutative measure and integration, Noncommutative algebraic geometry, Probability measures on groups or semigroups, Fourier transforms, factorization Weingarten integration over noncommutative homogeneous spaces
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative projective geometry; generalized Weyl algebra; graded module category; category equivalence Graded rings and modules (associative rings and algebras), Module categories in associative algebras, Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry The noncommutative schemes of generalized Weyl algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Koszul complex; homomorphism of symmetric algebras; almost complete intersection; Rees ring Restuccia G.,Formes linéaires et algèbres symétriques, Bull. Sc. Math.,110 (1986), 391--410. Homological conjectures (intersection theorems) in commutative ring theory, Complete intersections, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) Linear forms and symmetric algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces graded Lie algebras; spherical varieties Group actions on varieties or schemes (quotients), Homogeneous spaces and generalizations, Simple, semisimple, reductive (super)algebras Commutative subalgebras and sphericity in \({\mathbb Z}_2\)-graded Lie algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Model quantum field theories, Noncommutative geometry methods in quantum field theory, Grassmannians, Schubert varieties, flag manifolds, Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) Noncommutative Grassmannian \(U(1)\) sigma-model and Bargmann-Fock space
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Research exposition (monographs, survey articles) pertaining to algebraic geometry, Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry, Categories in geometry and topology Noncommutative geometry. A functorial approach
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative tori; Anasov automorphisms; C*-algebras; K-theory; cluster C*-algebras; Sklyanin algebras; AF-algebras; UHF-algebras; Hecke eigenform; continuous geometries; Connes geometries; index theory; Kasparov KK-theory; Jones polynomials; quantum groups; Hopf algebra; noncommutative algebraic geometry; deformation quantization Research exposition (monographs, survey articles) pertaining to algebraic geometry, Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry, Categories in geometry and topology Noncommutative geometry. A functorial approach
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Brauer's \(n\)-diagrams; matrix representation; orthogonal group; enveloping algebra; adjoint functor ------, Symmetric self-adjunctions: A justification of Brauer's representation of Brauer's algebras, Proceedings of the Conference ''Contemporary Geometry and Related Topics'' (N. Bokan et al., editors), Faculty of Mathematics, Belgrade, 2006, pp. 177-187 Group actions on varieties or schemes (quotients), General low-dimensional topology, Representation theory of groups, Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) Symmetric self-adjunctions: a justification of Brauer's representation of Brauer's algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces tropical algebra; tropical semiring; extended semiring; supertropical semiring; fundamental theorem of symmetric polynomials Semirings, Symbolic computation and algebraic computation Symmetric polynomials in tropical algebra semirings
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Noncommutative geometry in quantum theory, Covariant wave equations in quantum theory, relativistic quantum mechanics, Representations of Lie algebras and Lie superalgebras, analytic theory, Structure and representation of the Lorentz group, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Special relativity, Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics, Formal methods and deformations in algebraic geometry, Conformal structures on manifolds Spinorial Snyder and Yang models from superalgebras and noncommutative quantum superspaces
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces vertex algebras; chiral algebras; factorization algebras; Borcherds's approach Chiral algebras, factorization algebras, and Borcherds's ``singular commutative rings'' approach to vertex algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Schur functions; Schubert polynomials; nilplaxtic relation; alphabet; monoid; word; Schensted construction; Coxeter relations; transpositions; nilplaxtic classes; standard tableaux; sums of tableaux; reduced decompositions Lascoux, A.; Schützenberger, M. P., Tableaux and noncommutative Schubert polynomials, Funct. Anal. Appl., 23, 223-225, (1990) Representations of finite symmetric groups, Free semigroups, generators and relations, word problems, Combinatorial aspects of representation theory, Grassmannians, Schubert varieties, flag manifolds, Combinatorial identities, bijective combinatorics, Symmetric functions and generalizations Noncommutative Schubert polynomials
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces semidefinite programming; Grassmannian; maximum likelihood degree; Algebraic statistics; linear concentration model; coisotropic hypersurface Algebraic statistics, Grassmannians, Schubert varieties, flag manifolds, Determinantal varieties, Semidefinite programming Linear spaces of symmetric matrices with non-maximal maximum likelihood degree
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces zeta functions; \(l\)-adic cohomology; zeta functions of cycles Zeta and \(L\)-functions in characteristic \(p\), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Zeta functions of certain noncommutative algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces equivariant tilting module; Pfaffian variety; matrix factorization Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Derived categories, triangulated categories, Derived categories and associative algebras Equivariant tilting modules, Pfaffian varieties and noncommutative matrix factorizations
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Euclidean space; Riemannian geometry; Clifford torus; Poisson structures; scalar curvature; geometric modules Arnlind, J, Curvature and geometric modules of noncommutative spheres and tori, J. Math. Phys., 55, 041705, (2014) Poisson manifolds; Poisson groupoids and algebroids, Noncommutative algebraic geometry, Poisson algebras Curvature and geometric modules of noncommutative spheres and tori
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Azumaya algebra; Brauer group; noncommutative residue; pseudo differential symbol M. Wodzicki, Noncommutative residue. Chapter IV. Homology of algebras of differential operators and symbols , (in preparation). Noncommutative global analysis, noncommutative residues, Brauer groups (algebraic aspects), Positive characteristic ground fields in algebraic geometry, Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.), Noncommutative geometry (à la Connes) Algebras of \(p\)-symbols, noncommutative \(p\)-residue, and the Brauer group
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Koszul dual algebra; Morita autoequivalence; derived category of coherent sheaves Polishchuk, A., Noncommutative two-tori with real multiplication as noncommutative projective varieties, J. Geom. Phys., 50, 162-187, (2004) Noncommutative algebraic geometry, Elliptic curves, Rings arising from noncommutative algebraic geometry, Noncommutative geometry (à la Connes) Noncommutative two-tori with real multiplication as noncommutative projective varieties
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces deforming algebras of functions; quantum groups; noncommutative spaces; categories of graded modules Vancliff M., Algebras and representation theory Graded rings and modules (associative rings and algebras), Quantum groups (quantized enveloping algebras) and related deformations, Noncommutative algebraic geometry, Clifford algebras, spinors, Rings arising from noncommutative algebraic geometry, Quantum groups and related algebraic methods applied to problems in quantum theory Non-commutative spaces for graded quantum groups and graded Clifford algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces semisimple Lie algebra; symmetric pair; commuting variety; nilpotent orbit Bulois, M., Composantes irréductibles de la variété commutante nilpotente d'une algèbre de Lie symétrique semi-simple, Ann. inst. Fourier, 59, 37-80, (2009) Coadjoint orbits; nilpotent varieties, Simple, semisimple, reductive (super)algebras, Group actions on varieties or schemes (quotients) Irreducible components of the nilpotent commuting variety of a symmetric semisimple Lie algebra
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces prehomogeneous vector spaces of commutative parabolic type; prehomogeneous vector spaces of parabolic type; functional equations; zeta functions; parabolic subalgebras; semisimple Lie algebras Rubenthaler H., Algèbres de Lie et Espaces Préhomogènes (1992) Simple, semisimple, reductive (super)algebras, Grassmannians, Schubert varieties, flag manifolds, Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras Lie algebras and prehomogeneous vector spaces
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces non-commutative algebras; locally free sheaves; integral scheme R. Miranda and M. Teicher,Non-commutative algebras of dimension three over integral schemes, Trans. Am. Math. Soc.292 (1985), 705--712. Generalizations (algebraic spaces, stacks), Finite rings and finite-dimensional associative algebras Noncommutative algebras of dimension three over integral schemes
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Van den Bergh, M.: Noncommutative quadrics. Int. Math. Res. Not. IMRN \textbf{17}, 3983-4026 (2011) Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry Noncommutative quadrics
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces \(*\)-algebra; Fejér-Riesz theorem; unilateral shift operator; noncommutative positivstellensatz; Toeplitz algebra Savchuk, Y.; Schmüdgen, K.: A noncommutative version of the Fejér-Riesz theorem, Proc. amer. Math. soc. 138, No. 4, 1243-1248 (2010) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, Noncommutative algebraic geometry, Trigonometric polynomials, inequalities, extremal problems, Linear operators in \({}^*\)-algebras, Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) A noncommutative version of the Fejér-Riesz theorem
| 0 |
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