Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2018, Volume 50, Issue 1, pp. 159 - 165

Let A be a central quantization of an affine Poisson variety X over a field of characteristic p>0. We show that the completion of A with repect to a closed...

16W70 (primary) | 16S80 | 17B63 (secondary) | MATHEMATICS

16W70 (primary) | 16S80 | 17B63 (secondary) | MATHEMATICS

Journal Article

Reports on Mathematical Physics, ISSN 0034-4877, 10/2017, Volume 80, Issue 2, pp. 161 - 176

In this paper we provide an exposition on integrability theorem and relation between D-modules and symplectic geometry. We prove that the characteristic ideal...

Primary 16W70 | characteristic ideal | Poisson bracket | Secondary 16W50 | characteristic variety | Weyl algebra | INTEGRABILITY | PHYSICS, MATHEMATICAL | Algebra

Primary 16W70 | characteristic ideal | Poisson bracket | Secondary 16W50 | characteristic variety | Weyl algebra | INTEGRABILITY | PHYSICS, MATHEMATICAL | Algebra

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 04/2008, Volume 142, Issue 3, pp. 465 - 510

We study the irregularity sheaves attached to the A-hypergeometric D-module MA introduced by I. M. Gel' fand and others in [GGZ], [GZK], where A is an element...

MATHEMATICS | RINGS | 13N10 | 14M25 | 16W70

MATHEMATICS | RINGS | 13N10 | 14M25 | 16W70

Journal Article

Georgian Mathematical Journal, ISSN 1072-947X, 09/2018, Volume 25, Issue 3, pp. 451 - 459

Let be the free algebra generated by over a field . It is shown that, with respect to any weighted -gradation attached to , minimal homogeneous generating sets...

Free algebra | homogeneous generating set | Gröbner basis | standard basis | 16Z05 | 16W70 | Grobner basis | MATHEMATICS | RESOLUTIONS | NONCOMMUTATIVE GROBNER BASES

Free algebra | homogeneous generating set | Gröbner basis | standard basis | 16Z05 | 16W70 | Grobner basis | MATHEMATICS | RESOLUTIONS | NONCOMMUTATIVE GROBNER BASES

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 12/2017, Volume 109, Issue 6, pp. 499 - 503

We observe that a finitely generated algebraic algebra R (over a field) is finite dimensional if and only if the associated graded ring $${{\text {gr}}}{R}$$...

Secondary 16N40 | Graded-nil subring | 16W70 | Algebraic algebra | Mathematics, general | Mathematics | Primary 16U99 | Associated graded algebra | NIL | MATHEMATICS | GROWTH | GELFAND-KIRILLOV DIMENSION | Algebra

Secondary 16N40 | Graded-nil subring | 16W70 | Algebraic algebra | Mathematics, general | Mathematics | Primary 16U99 | Associated graded algebra | NIL | MATHEMATICS | GROWTH | GELFAND-KIRILLOV DIMENSION | Algebra

Journal Article

Forum Mathematicum, ISSN 0933-7741, 07/2019, Volume 31, Issue 4, pp. 867 - 905

We explore the graded-formality and filtered-formality properties of finitely generated groups by studying the various Lie algebras over a field of...

Chen Lie algebra | Malcev Lie algebra | 1-formality | 20J05 | holonomy Lie algebra | 16W70 | 55P62 | Seifert manifold | filtered-formality | 20F40 | 57M05 | graded-formality | 20F18 | nilpotent group | 17B70 | minimal model | Central series | 20F14 | 16S37 | TOPOLOGY | MATHEMATICS, APPLIED | SPACES | CUP PRODUCTS | LOWER CENTRAL SERIES | PRESENTATIONS | NILMANIFOLDS | MATHEMATICS | COMPLETION | RATIONAL HOMOTOPY-THEORY | HOMOLOGY | GEOMETRY | Algebra | Fields (mathematics) | Quotients | Group theory | Lie groups

Chen Lie algebra | Malcev Lie algebra | 1-formality | 20J05 | holonomy Lie algebra | 16W70 | 55P62 | Seifert manifold | filtered-formality | 20F40 | 57M05 | graded-formality | 20F18 | nilpotent group | 17B70 | minimal model | Central series | 20F14 | 16S37 | TOPOLOGY | MATHEMATICS, APPLIED | SPACES | CUP PRODUCTS | LOWER CENTRAL SERIES | PRESENTATIONS | NILMANIFOLDS | MATHEMATICS | COMPLETION | RATIONAL HOMOTOPY-THEORY | HOMOLOGY | GEOMETRY | Algebra | Fields (mathematics) | Quotients | Group theory | Lie groups

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 6/2018, Volume 21, Issue 3, pp. 605 - 625

The ADR algebra R A of an Artin algebra A is a right ultra strongly quasihereditary algebra (RUSQ algebra). In this paper we study the Δ-filtrations of modules...

Quasihereditary algebra | ADR algebra | Associative Rings and Algebras | 16S50 | Non-associative Rings and Algebras | 16W70 | Commutative Rings and Algebras | Mathematics | Strongly quasihereditary algebra | 16G20 | 16G10 | MATHEMATICS | MODULES | Mathematics - Representation Theory

Quasihereditary algebra | ADR algebra | Associative Rings and Algebras | 16S50 | Non-associative Rings and Algebras | 16W70 | Commutative Rings and Algebras | Mathematics | Strongly quasihereditary algebra | 16G20 | 16G10 | MATHEMATICS | MODULES | Mathematics - Representation Theory

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 7/2014, Volume 174, Issue 3, pp. 403 - 412

To a multi-index filtration (say, on the ring of germs of functions on a germ of a complex analytic variety) one associates several invariants: the Hilbert...

Plane valuations | Hilbert functions | Poincaré series | 16W70 | Mathematics, general | Mathematics | Filtrations | 13A18 | 14B05

Plane valuations | Hilbert functions | Poincaré series | 16W70 | Mathematics, general | Mathematics | Filtrations | 13A18 | 14B05

Journal Article

Ars Mathematica Contemporanea, ISSN 1855-3966, 2019, Volume 16, Issue 2, pp. 319 - 329

The space of linearly recursive sequences of complex numbers admits two distinguished topologies. Namely, the adic topology induced by the ideal of those...

Adic topologies | Linearly recursive sequences | Hopf algebras | Power series | MATHEMATICS | MATHEMATICS, APPLIED | power series | adic topologies

Adic topologies | Linearly recursive sequences | Hopf algebras | Power series | MATHEMATICS | MATHEMATICS, APPLIED | power series | adic topologies

Journal Article

Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 3/2019, Volume 25, Issue 1, pp. 87 - 96

Let R be a ring and $$\delta $$ δ is a derivation of R. In this paper, it is proved that, under suitable conditions, the differential polynomial ring...

Semicentral idempotent | Piecewise prime ring | Primary 16W60 | Secondary 16P40 | Quasi-Baer ring | Differential polynomial ring | Triangulating dimension | 16W70 | Generalized triangular matrix representation | Mathematics, general | Mathematics | 16S36

Semicentral idempotent | Piecewise prime ring | Primary 16W60 | Secondary 16P40 | Quasi-Baer ring | Differential polynomial ring | Triangulating dimension | 16W70 | Generalized triangular matrix representation | Mathematics, general | Mathematics | 16S36

Journal Article

11.
Full Text
Topological tensor product of bimodules, complete Hopf algebroids and convolution algebras

Communications in Contemporary Mathematics, ISSN 0219-1997, 09/2019, Volume 21, Issue 6, p. 1850015

Given a finitely generated and projective Lie–Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids between...

co-commutative Hopf algebroids | Complete commutative Hopf algebroids | Lie algebroids | completion 2-functor | topological tensor product | adic topology | convolution algebras | filtered bimodules | finite dual | Lie–Rinehart algebras | MATHEMATICS | MATHEMATICS, APPLIED | Lie-Rinehart algebras | Algebra

co-commutative Hopf algebroids | Complete commutative Hopf algebroids | Lie algebroids | completion 2-functor | topological tensor product | adic topology | convolution algebras | filtered bimodules | finite dual | Lie–Rinehart algebras | MATHEMATICS | MATHEMATICS, APPLIED | Lie-Rinehart algebras | Algebra

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 5/2015, Volume 28, Issue 2, pp. 449 - 467

We define a new equivariant (with respect to a finite group $$G$$ G action) version of the Poincaré series of a multi-index filtration as an element of the...

16W70 | Mathematics | Filtrations | Topology | 13A18 | Monodromy zeta functions | Finite group actions | 14B05 | Geometry | Algebra | Plane valuations | Analysis | Poincaré series | Mathematics, general | Applications of Mathematics | 16W22

16W70 | Mathematics | Filtrations | Topology | 13A18 | Monodromy zeta functions | Finite group actions | 14B05 | Geometry | Algebra | Plane valuations | Analysis | Poincaré series | Mathematics, general | Applications of Mathematics | 16W22

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 4/2018, Volume 21, Issue 2, pp. 375 - 397

An off-shell representation of supersymmetry is a representation of the super Poincaré algebra on a dynamically unconstrained space of fields. We describe such...

Filtration | Bifiltration | Super Poincaré | Secondary: 15A66 | Non-associative Rings and Algebras | Adinkra | 16W70 | Commutative Rings and Algebras | Mathematics | Supersymmetric quantum mechanics | Associative Rings and Algebras | Spinor | Clifford algebra | Primary: 81Q60 | Off-shell supersymmetry | Super Poincare | MATHEMATICS | Quantum theory | Algebra

Filtration | Bifiltration | Super Poincaré | Secondary: 15A66 | Non-associative Rings and Algebras | Adinkra | 16W70 | Commutative Rings and Algebras | Mathematics | Supersymmetric quantum mechanics | Associative Rings and Algebras | Spinor | Clifford algebra | Primary: 81Q60 | Off-shell supersymmetry | Super Poincare | MATHEMATICS | Quantum theory | Algebra

Journal Article

Czechoslovak Mathematical Journal, ISSN 0011-4642, 12/2015, Volume 65, Issue 4, pp. 1011 - 1022

Let K be a field and S = K[x 1, …, x m , y 1,…, y n ] be the standard bigraded polynomial ring over K. In this paper, we explicitly describe the structure of...

dimension filtration | 16W50 | sequentially Cohen-Macaulay filtration | 16W70 | 13D45 | Mathematics | Cohen-Macaulay module | 13C14 | bigraded module | Ordinary Differential Equations | cohomological dimension | Analysis | Convex and Discrete Geometry | Mathematics, general | Mathematical Modeling and Industrial Mathematics | MATHEMATICS

dimension filtration | 16W50 | sequentially Cohen-Macaulay filtration | 16W70 | 13D45 | Mathematics | Cohen-Macaulay module | 13C14 | bigraded module | Ordinary Differential Equations | cohomological dimension | Analysis | Convex and Discrete Geometry | Mathematics, general | Mathematical Modeling and Industrial Mathematics | MATHEMATICS

Journal Article

Journal of Homotopy and Related Structures, ISSN 2193-8407, 9/2018, Volume 13, Issue 3, pp. 599 - 633

Our objective is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of a...

Persistent homology | Algebraic Topology | 16W70 | Mathematics | dg algebras | 16E45 | 18G55 | 55U10 | Algebra | Functional Analysis | A_{\infty }$$ A ∞ -algebras | Bottleneck metric | Number Theory | algebras | MATHEMATICS | ALGEBRAS | A(infinity)-algebras | HOMOLOGY | K-Theory and Homology

Persistent homology | Algebraic Topology | 16W70 | Mathematics | dg algebras | 16E45 | 18G55 | 55U10 | Algebra | Functional Analysis | A_{\infty }$$ A ∞ -algebras | Bottleneck metric | Number Theory | algebras | MATHEMATICS | ALGEBRAS | A(infinity)-algebras | HOMOLOGY | K-Theory and Homology

Journal Article

Journal of Commutative Algebra, ISSN 1939-0807, 12/2014, Volume 6, Issue 4, pp. 485 - 504

Given a finitely generated module 𝑀 over a commutative local ring (or a standard graded 𝑘-algebra) (𝑅, 𝔪, 𝑘), we detect its complexity in terms of...

Koszul algebras | Linearity defect | Standard basis | Minimal free resolutions | Filtered modules | Associated graded module | Regularity | linearity defect | filtered modules | MATHEMATICS | ALGEBRA | minimal free resolutions | standard basis | associated graded module

Koszul algebras | Linearity defect | Standard basis | Minimal free resolutions | Filtered modules | Associated graded module | Regularity | linearity defect | filtered modules | MATHEMATICS | ALGEBRA | minimal free resolutions | standard basis | associated graded module

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 1/2013, Volume 26, Issue 1, pp. 241 - 251

We offer a new approach to a definition of an equivariant version of the Poincaré series. This Poincaré series is defined not as a power series, but as an...

16W70 | Mathematics | Filtrations | Topology | Finite group actions | 14B05 | Geometry | Algebra | Analysis | Poincaré series | Mathematics, general | Applications of Mathematics | 16W22

16W70 | Mathematics | Filtrations | Topology | Finite group actions | 14B05 | Geometry | Algebra | Analysis | Poincaré series | Mathematics, general | Applications of Mathematics | 16W22

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2013, Volume 63, Issue 3, pp. 923 - 956

We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of 'quantum' type in all but a few exceptional cases.

Global dimension | Hochschild cohomology | Generalized Weyl algebra | MATHEMATICS | global dimension | generalized Weyl algebra | SMOOTHNESS | Mathematics - K-Theory and Homology

Global dimension | Hochschild cohomology | Generalized Weyl algebra | MATHEMATICS | global dimension | generalized Weyl algebra | SMOOTHNESS | Mathematics - K-Theory and Homology

Journal Article

manuscripta mathematica, ISSN 0025-2611, 11/2006, Volume 121, Issue 3, pp. 385 - 410

We introduce pretty clean modules, extending the notion of clean modules by Dress, and show that pretty clean modules are sequentially Cohen–Macaulay. We also...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 16W70 | Algebraic Geometry | Mathematics, general | 13C13 | Mathematics | Number Theory | 05E99 | 13C14 | MATHEMATICS | BOUNDS

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 16W70 | Algebraic Geometry | Mathematics, general | 13C13 | Mathematics | Number Theory | 05E99 | 13C14 | MATHEMATICS | BOUNDS

Journal Article

Journal of Homotopy and Related Structures, ISSN 2193-8407, 9/2017, Volume 12, Issue 3, pp. 513 - 548

Lapin has constructed a multiplicative spectral sequence from a deformation of an $$A_{\infty }$$ A ∞ -algebra. In particular, as noted by the same author, one...

Spectral sequences | Dg algebras | Algebraic Topology | 16W70 | Mathematics | 16S80 | 16E45 | 18G55 | 14D15 | 18G40 | Algebra | Homological algebra | Functional Analysis | A_{\infty }$$ A ∞ -algebras | Number Theory | 55T05 | algebras | MATHEMATICS | A infinity-algebras | ALGEBRAS | K-Theory and Homology

Spectral sequences | Dg algebras | Algebraic Topology | 16W70 | Mathematics | 16S80 | 16E45 | 18G55 | 14D15 | 18G40 | Algebra | Homological algebra | Functional Analysis | A_{\infty }$$ A ∞ -algebras | Number Theory | 55T05 | algebras | MATHEMATICS | A infinity-algebras | ALGEBRAS | K-Theory and Homology

Journal Article

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