Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2019, Volume 21, Issue 8, p. 1850069

We construct three families of vertex algebras along with their modules from appropriate vertex Lie algebras, using the constructions in [Vertex Lie algebra,...

Bakas-Block algebra | vertex Lie algebra | polynomial Virasoro algebra | vertex tensor category | β γ -system | Strongly graded vertex algebra | C 1 A -cofiniteness condition | INVARIANCE | MATHEMATICS, APPLIED | REPRESENTATIONS | EQUATIONS | MATHEMATICS | C-1(A)-cofiniteness condition | SYSTEMS | QUASIFINITE MODULES | beta gamma-system | Algebra

Bakas-Block algebra | vertex Lie algebra | polynomial Virasoro algebra | vertex tensor category | β γ -system | Strongly graded vertex algebra | C 1 A -cofiniteness condition | INVARIANCE | MATHEMATICS, APPLIED | REPRESENTATIONS | EQUATIONS | MATHEMATICS | C-1(A)-cofiniteness condition | SYSTEMS | QUASIFINITE MODULES | beta gamma-system | Algebra

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 05/2018, Volume 17, Issue 5

In this paper, we introduce and study differential graded (DG) down-up algebras. In brief, a DG down-up algebra A is a connected cochain DC algebra such that...

Graded down-up algebra | Isomorphism problem | Calabi-Yau DG algebra | DG algebra | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | SPACES | RINGS | EVALUATION MAP | isomorphism problem | DIFFERENTIAL GRADED ALGEBRAS

Graded down-up algebra | Isomorphism problem | Calabi-Yau DG algebra | DG algebra | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | SPACES | RINGS | EVALUATION MAP | isomorphism problem | DIFFERENTIAL GRADED ALGEBRAS

Journal Article

Journal of Algebra, ISSN 0021-8693, 04/2017, Volume 475, pp. 327 - 360

The representations of a quiver Q over a field k (the kQ-modules, where kQ is the path algebra of Q over k) have been studied for a long time, and one knows...

Triangulated category of singularities | Perfect complexes | Gorenstein-projective modules | Relationship between abelian categories and triangulated categories | Homotopy category | Graded group algebras | Differential modules | Ghost maps | Torsionless modules | Perfect differential modules | Derived category | Auslander–Reiten quiver of Gorenstein-projective modules | Dual numbers | Covering theory | Gorenstein algebras | Frobenius category | Finite acyclic quivers and their representations over an algebra | Homology functor | Strongly Gorenstein-projective modules | Triangulated category of | SUBCATEGORIES | DIFFERENTIAL MODULES | Strongly Gorenstein-projective | singularities | modules Differential modules | GORENSTEIN | CATEGORIES | MATHEMATICS | Finite acyclic quivers and their | representations over an algebra | Statistics | Algebra

Triangulated category of singularities | Perfect complexes | Gorenstein-projective modules | Relationship between abelian categories and triangulated categories | Homotopy category | Graded group algebras | Differential modules | Ghost maps | Torsionless modules | Perfect differential modules | Derived category | Auslander–Reiten quiver of Gorenstein-projective modules | Dual numbers | Covering theory | Gorenstein algebras | Frobenius category | Finite acyclic quivers and their representations over an algebra | Homology functor | Strongly Gorenstein-projective modules | Triangulated category of | SUBCATEGORIES | DIFFERENTIAL MODULES | Strongly Gorenstein-projective | singularities | modules Differential modules | GORENSTEIN | CATEGORIES | MATHEMATICS | Finite acyclic quivers and their | representations over an algebra | Statistics | Algebra

Journal Article

4.
Full Text
RANK TWO TOPOLOGICAL AND INFINITESIMAL EMBEDDED JUMP LOCI OF QUASI-PROJECTIVE MANIFOLDS

Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 02/2018, Volume 19, Issue 2, pp. 1 - 35

We study the germs at the origin of G -representation varieties and the degree 1 cohomology jump loci of fundamental groups of quasi-projective manifolds....

admissible map | representation variety | differential graded algebra model | quasi-projective manifold | holonomy Lie algebra | semisimple Lie algebra | cohomology jump loci | analytic germ | Deligne weight filtration | variety of flat connections | REPRESENTATIONS | VARIETIES | MATHEMATICS | COHOMOLOGY | GEOMETRY | Homology | Inclusions | Loci | Subgroups | Linear algebra

admissible map | representation variety | differential graded algebra model | quasi-projective manifold | holonomy Lie algebra | semisimple Lie algebra | cohomology jump loci | analytic germ | Deligne weight filtration | variety of flat connections | REPRESENTATIONS | VARIETIES | MATHEMATICS | COHOMOLOGY | GEOMETRY | Homology | Inclusions | Loci | Subgroups | Linear algebra

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 2/2018, Volume 13, Issue 1, pp. 173 - 185

Let A be a path A ∞-algebra over a positively graded quiver Q: We prove that the derived category of A is triangulated equivalent to the derived category of...

Koszul dual | 18E30 | Mathematics, general | Mathematics | A ∞ -algebras | DG-algebras | 16E45 | MATHEMATICS | A(infinity)-algebras | Mathematical analysis | Algebra | Differential equations

Koszul dual | 18E30 | Mathematics, general | Mathematics | A ∞ -algebras | DG-algebras | 16E45 | MATHEMATICS | A(infinity)-algebras | Mathematical analysis | Algebra | Differential equations

Journal Article

Advances in Mathematics, ISSN 0001-8708, 03/2013, Volume 235, pp. 92 - 125

We prove that, on a smooth projective variety over an algebraically closed field of characteristic 0, the semiregularity map annihilates every obstruction to...

Obstruction theory | DG-schemes | Differential graded Lie algebras | Local cohomology | Deformation theory | LIE-ALGEBRAS | MATHEMATICS | MODULES | FUNCTORS | COMPACT KAHLER-MANIFOLDS | MAP | DEFORMATION-THEORY | Algebra

Obstruction theory | DG-schemes | Differential graded Lie algebras | Local cohomology | Deformation theory | LIE-ALGEBRAS | MATHEMATICS | MODULES | FUNCTORS | COMPACT KAHLER-MANIFOLDS | MAP | DEFORMATION-THEORY | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 06/2018, Volume 46, Issue 6, pp. 2714 - 2729

In this paper, the so-called differential graded (DG for short) Poisson Hopf algebra is introduced, which can be considered as a natural extension of Poisson...

differential graded Poisson algebras | Differential graded Hopf algebras | differential graded Poisson Hopf algebras | universal enveloping algebras | MATHEMATICS | Algebra

differential graded Poisson algebras | Differential graded Hopf algebras | differential graded Poisson Hopf algebras | universal enveloping algebras | MATHEMATICS | Algebra

Journal Article

Homology, Homotopy and Applications, ISSN 1532-0073, 2011, Volume 13, Issue 2, pp. 175 - 195

We give a construction of an L-infinity map from any L-infinity algebra into its truncated Chevalley-Eilenberg complex as well as its cyclic and A(infinity)...

Morita equivalence | Graph homology | A-infinity algebra | Differential graded lie algebra | Maurer-Cartan element | MATHEMATICS | MATHEMATICS, APPLIED | graph homology | differential graded Lie algebra | HOMOTOPY ALGEBRAS | A_\infty algebra | 18D50 | 57T30 | Differential graded Lie algebra | 16E45 | 81T18

Morita equivalence | Graph homology | A-infinity algebra | Differential graded lie algebra | Maurer-Cartan element | MATHEMATICS | MATHEMATICS, APPLIED | graph homology | differential graded Lie algebra | HOMOTOPY ALGEBRAS | A_\infty algebra | 18D50 | 57T30 | Differential graded Lie algebra | 16E45 | 81T18

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 11/2019, Volume 42, Issue 6, pp. 3343 - 3377

For any differential graded (DG for short) Poisson algebra A given by generators and relations, we give a “formula” for computing the universal enveloping...

Universal enveloping algebras | 16S10 | 17B35 | 17B63 | Simple differential graded Poisson module | Mathematics, general | Differential graded Poisson algebras | Mathematics | Applications of Mathematics | PBW-basis | 16E45 | MATHEMATICS | Polynomials | Algebra

Universal enveloping algebras | 16S10 | 17B35 | 17B63 | Simple differential graded Poisson module | Mathematics, general | Differential graded Poisson algebras | Mathematics | Applications of Mathematics | PBW-basis | 16E45 | MATHEMATICS | Polynomials | Algebra

Journal Article

2018, ISBN 3319968262, 604

This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic...

Geometry, Algebraic-Data processing

Geometry, Algebraic-Data processing

eBook

Journal of Homotopy and Related Structures, ISSN 2193-8407, 6/2016, Volume 11, Issue 2, pp. 153 - 172

We prove that the rational homotopy type of the complement of the graph of a continuous map from a simply connected closed manifold to a 2-connected closed...

Minimal model | Algebraic Topology | Commutative differential graded algebra | 55P62 | Mathematics | Leray spectral sequence | Formal space and map | 55N30 | Algebra | Functional Analysis | 55R20 | Sullivan model | 55M05 | Number Theory | 55U25 | MATHEMATICS | CONFIGURATION-SPACES | MODELS

Minimal model | Algebraic Topology | Commutative differential graded algebra | 55P62 | Mathematics | Leray spectral sequence | Formal space and map | 55N30 | Algebra | Functional Analysis | 55R20 | Sullivan model | 55M05 | Number Theory | 55U25 | MATHEMATICS | CONFIGURATION-SPACES | MODELS

Journal Article

Proceedings - Mathematical Sciences, ISSN 0253-4142, 4/2019, Volume 129, Issue 2, pp. 1 - 20

Starting with a spectral triple, one can associate two canonical differential graded algebras (DGA) defined by Connes (Noncommutative geometry (1994) Academic...

quantum double suspension | Primary: 58B34 | Mathematics, general | Mathematics | Connes’ calculus | spectral triple | 16E45 | Dirac differential graded algebra | FGR differential graded algebra | Secondary: 46L87 | SPECTRAL TRIPLES | MATHEMATICS | QUANTUM | Connes' calculus | Geometry | Algebra | Research | Mathematical research

quantum double suspension | Primary: 58B34 | Mathematics, general | Mathematics | Connes’ calculus | spectral triple | 16E45 | Dirac differential graded algebra | FGR differential graded algebra | Secondary: 46L87 | SPECTRAL TRIPLES | MATHEMATICS | QUANTUM | Connes' calculus | Geometry | Algebra | Research | Mathematical research

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 2018, Volume 16, Issue 2

Graded bundles are a particularly nice class of graded manifolds and represent a natural generalization of vector bundles. By exploiting the formalism of...

Lie algebroids | Graded bundles | actions | connections | double vector bundles | BUNDLES | MECHANICAL SYSTEMS | CATEGORY | PHYSICS, MATHEMATICAL

Lie algebroids | Graded bundles | actions | connections | double vector bundles | BUNDLES | MECHANICAL SYSTEMS | CATEGORY | PHYSICS, MATHEMATICAL

Journal Article

Compositio Mathematica, ISSN 0010-437X, 08/2015, Volume 151, Issue 8, pp. 1499 - 1528

To study infinitesimal deformation problems with cohomology constraints, we introduce and study cohomology jump functors for differential graded Lie algebra...

cohomology jump locus | deformation theory | differential graded Lie algebra | local system | MATHEMATICS | MODULI SPACE | Algebra | Deformation | Mathematical analysis | Lie groups | Representations | Vectors (mathematics) | Loci | Bundles | Mathematics - Algebraic Geometry

cohomology jump locus | deformation theory | differential graded Lie algebra | local system | MATHEMATICS | MODULI SPACE | Algebra | Deformation | Mathematical analysis | Lie groups | Representations | Vectors (mathematics) | Loci | Bundles | Mathematics - Algebraic Geometry

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 07/2012, Volume 23, Issue 7, pp. 1250053 - 1250030

We identify dglas that control infinitesimal deformations of the pairs (manifold, Higgs bundle) and of Hitchin pairs. As a consequence, we recover known...

algebras | Hitchin pairs | differential graded Lie algebras | Deformation theory | MATHEMATICS | COMPACT KAHLER-MANIFOLDS | L-infinity-algebras | MODULI | Bundling | Manifolds | Descriptions | Obstructions | Deformation | Mathematical analysis | Standards

algebras | Hitchin pairs | differential graded Lie algebras | Deformation theory | MATHEMATICS | COMPACT KAHLER-MANIFOLDS | L-infinity-algebras | MODULI | Bundling | Manifolds | Descriptions | Obstructions | Deformation | Mathematical analysis | Standards

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2016, Volume 59, Issue 5, pp. 849 - 860

We introduce the notions of differential graded（DG） Poisson algebra and DG Poisson module. Let A be any DG Poisson algebra. We construct the universal...

UE | 微分几何 | 代数结构 | 包络代数 | 范畴同构 | 同调代数 | 代数和 | 模块 | differential graded Poisson algebras | differential graded algebras | differential graded Hopf algebras | differential graded Lie algebras | universal enveloping algebras | monoidal category | Algebra | Construction | Tensors | Categories | Mathematical analysis | Modules | Paper | Homology | Mathematics - Rings and Algebras

UE | 微分几何 | 代数结构 | 包络代数 | 范畴同构 | 同调代数 | 代数和 | 模块 | differential graded Poisson algebras | differential graded algebras | differential graded Hopf algebras | differential graded Lie algebras | universal enveloping algebras | monoidal category | Algebra | Construction | Tensors | Categories | Mathematical analysis | Modules | Paper | Homology | Mathematics - Rings and Algebras

Journal Article

Journal of Noncommutative Geometry, ISSN 1661-6952, 2015, Volume 9, Issue 2, pp. 543 - 565

We develop the theory of linear algebra over a (Z(2))(n)-commutative algebra (n is an element of N), which includes the well-known super linear algebra as a...

Graded trace and Berezinian | Graded linear algebra | Clifford algebra | Quaternions | MATHEMATICS | MATHEMATICS, APPLIED | graded trace and Berezinian | quaternions | ALGEBRAS | PHYSICS, MATHEMATICAL

Graded trace and Berezinian | Graded linear algebra | Clifford algebra | Quaternions | MATHEMATICS | MATHEMATICS, APPLIED | graded trace and Berezinian | quaternions | ALGEBRAS | PHYSICS, MATHEMATICAL

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2005, Volume 2005, Issue 62, pp. 3899 - 3918

We show that the HochschildKostantRosenberg map from the space of multivector fields on a graded manifold N (endowed with a Berezinian volume) to the...

MATHEMATICS | STRING TOPOLOGY | COHOMOLOGY | QUANTIZATION | DEFORMATION | GEOMETRY | Mathematics - Quantum Algebra

MATHEMATICS | STRING TOPOLOGY | COHOMOLOGY | QUANTIZATION | DEFORMATION | GEOMETRY | Mathematics - Quantum Algebra

Journal Article

Journal of Noncommutative Geometry, ISSN 1661-6952, 2009, Volume 3, Issue 4, pp. 579 - 597

For every compact Kahler manifold we give a canonical extension of Griffith's period map to generalized deformations, intended as solutions of Maurer-Cartan...

Kähler manifolds | Differential graded lie algebras | Functors of artin rings | Symmetric coalgebras | L∞-algebras | Period map | LIE-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | functors of Artin rings | symmetric coalgebras | Kahler manifolds | MANIFOLDS | Differential graded Lie algebras | L-infinity-algebras | PHYSICS, MATHEMATICAL | period map

Kähler manifolds | Differential graded lie algebras | Functors of artin rings | Symmetric coalgebras | L∞-algebras | Period map | LIE-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | functors of Artin rings | symmetric coalgebras | Kahler manifolds | MANIFOLDS | Differential graded Lie algebras | L-infinity-algebras | PHYSICS, MATHEMATICAL | period map

Journal Article

Journal of Zhejiang University, Science Edition, ISSN 1008-9497, 05/2016, Volume 43, Issue 3, pp. 253 - 263

Journal Article

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