Compositio mathematica, ISSN 0010-437X, 09/2015, Volume 151, Issue 9, pp. 1763 - 1790

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an $L_{\infty }$-algebra, which...

generalized complex manifold | deformation | Dirac manifold | Maurer-Cartan equation | Lz-algebra | Poisson manifold | BRACKETS | COISOTROPIC SUBMANIFOLDS | Maurer Cartan equation | BIALGEBROIDS | L-INFINITY-ALGEBRAS | QUASI | LIE-ALGEBRAS | MATHEMATICS | COMPLEX ANALYTIC STRUCTURES | L-infinity-algebra | MANIFOLDS | QUANTIZATION | Geometry | Theoretical mathematics | Construction | Deformation | Brackets | Machinery | Manifolds (mathematics) | Construction equipment

generalized complex manifold | deformation | Dirac manifold | Maurer-Cartan equation | Lz-algebra | Poisson manifold | BRACKETS | COISOTROPIC SUBMANIFOLDS | Maurer Cartan equation | BIALGEBROIDS | L-INFINITY-ALGEBRAS | QUASI | LIE-ALGEBRAS | MATHEMATICS | COMPLEX ANALYTIC STRUCTURES | L-infinity-algebra | MANIFOLDS | QUANTIZATION | Geometry | Theoretical mathematics | Construction | Deformation | Brackets | Machinery | Manifolds (mathematics) | Construction equipment

Journal Article

Journal of Algebra, ISSN 0021-8693, 09/2019, Volume 534, pp. 65 - 99

The main object of study of this paper is the notion of a LieDer pair, i.e. a Lie algebra with a derivation. We introduce the concept of a representation of a...

Deformations | Derivations | Lie 2-algebras | Central extensions | Cohomologies | Lie algebras | MATHEMATICS | MORPHISMS | Lic algebras | DEFORMATION-THEORY

Deformations | Derivations | Lie 2-algebras | Central extensions | Cohomologies | Lie algebras | MATHEMATICS | MORPHISMS | Lic algebras | DEFORMATION-THEORY

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 12/2015, Volume 219, Issue 12, pp. 5344 - 5362

We present a method to construct explicitly L∞-algebras governing simultaneous deformations of various kinds of algebraic structures and of their morphisms. It...

LIE-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | HOMOTOPY ALGEBRAS | Algebra

LIE-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | HOMOTOPY ALGEBRAS | Algebra

Journal Article

Advances in Mathematics, ISSN 0001-8708, 11/2016, Volume 303, pp. 954 - 1043

Associated to any manifold equipped with a closed form of degree >1 is an ‘L∞-algebra of observables’ which acts as a higher/homotopy analog of the Poisson...

Multisymplectic geometry | Strong homotopy Lie algebra | Moment map | Equivariant cohomology | MATHEMATICS | COURANT ALGEBROIDS | GEOMETRY | Analysis | Algebra

Multisymplectic geometry | Strong homotopy Lie algebra | Moment map | Equivariant cohomology | MATHEMATICS | COURANT ALGEBROIDS | GEOMETRY | Analysis | Algebra

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 11/2015, Volume 97, pp. 119 - 132

Given a Lie group acting on a manifold M preserving a closed n+1-form ω, the notion of homotopy moment map for this action was introduced in Fregier (0000), in...

N-plectic geometry | Lie algebras up to homotopy | Homotopy moment maps | FORMS | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | Algebra | Mathematics

N-plectic geometry | Lie algebras up to homotopy | Homotopy moment maps | FORMS | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | Algebra | Mathematics

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2011, Volume 2011, Issue 15, pp. 3471 - 3501

Our main goal in this paper is to translate the diagram below relating groups, Lie algebras, and Hopf algebras to the corresponding 2-objects, that is, to...

MATHEMATICS

MATHEMATICS

Journal Article

06/2018

Let $X$ be a smooth complex algebraic variety and let $\operatorname{Coh} (X)$ denote its Abelian category of coherent sheaves. By the work of W. Lowen and M....

Journal Article

06/2019

We propose an approach for transfer learning with GAN architectures. In general, transfer learning enables deep networks for classification tasks to be trained...

Journal Article

Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, 01/2008, Volume 15, Issue 2, pp. 252 - 269

Let M be an odd-dimensional Euclidean space endowed with a contact 1-form α. We investigate the space of symmetric contravariant tensor fields over M as a...

EQUIVARIANT SYMBOL CALCULUS | FORMS | LIE-ALGEBRA | QUANTIZATIONS | VECTOR-FIELDS | PHYSICS, MATHEMATICAL | DIFFERENTIAL-OPERATORS | MANIFOLD | Mathematics - Differential Geometry

EQUIVARIANT SYMBOL CALCULUS | FORMS | LIE-ALGEBRA | QUANTIZATIONS | VECTOR-FIELDS | PHYSICS, MATHEMATICAL | DIFFERENTIAL-OPERATORS | MANIFOLD | Mathematics - Differential Geometry

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2014, Volume 398, pp. 243 - 257

In this note we show that the theory of non-abelian extensions of a Lie algebra g by a Lie algebra h can be understood in terms of a differential graded Lie...

Deligne groupoid | Extensions | Lie algebras | Non-abelian cohomology | Maurer–Cartan equation | Maurer-Cartan equation | MATHEMATICS | Algebra

Deligne groupoid | Extensions | Lie algebras | Non-abelian cohomology | Maurer–Cartan equation | Maurer-Cartan equation | MATHEMATICS | Algebra

Journal Article

Journal of Generalized Lie Theory and Applications, ISSN 1736-5279, 2009, Volume 3, Issue 4, pp. 285 - 295

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 11/2004, Volume 70, Issue 2, pp. 97 - 107

We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a...

Geometry | homomorphisms | cohomology | Mathematical and Computational Physics | simultaneous | algebras | deformation | Group Theory and Generalizations | Physics | Statistical Physics | Homomorphisms | Deformation | Cohomology | Simultaneous | Algebras | PHYSICS, MATHEMATICAL

Geometry | homomorphisms | cohomology | Mathematical and Computational Physics | simultaneous | algebras | deformation | Group Theory and Generalizations | Physics | Statistical Physics | Homomorphisms | Deformation | Cohomology | Simultaneous | Algebras | PHYSICS, MATHEMATICAL

Journal Article

New York Journal of Mathematics, 2009, Volume 15, pp. 353 - 392

Journal Article

10/2013

In this note we show that the theory of non abelian extensions of a Lie algebra $\mathfrak{g}$ by a Lie algebra $\mathfrak{h}$ can be understood in terms of a...

Journal Article

10/2007

In recent years, algebras and modules of differential operators have been extensively studied. Equivariant quantization and dequantization establish a tight...

Journal Article

03/2019

Journal of Algebra 534 (2019) 65-99 The main object of study of this paper is the notion of a LieDer pair, i.e. a Lie algebra with a derivation. We introduce...

Journal Article

11/2018

In this article we apply ideas from homotopy theory to the study of singular foliations. We verify that a technical lemma remains valid for left semi-model...

Journal Article

06/2015

Given a graded associative algebra $A$, its lower central series is defined by $L_1 = A$ and $L_{i+1} = [L_i, A]$. We consider successive quotients $N_i(A) =...

Mathematics - Representation Theory

Mathematics - Representation Theory

Journal Article

2009, Volume 3, Issue 4

Publication

01/2013

Journal of Pure and Applied Algebra, Vol. 219 (2015), pp. 5344-5362 We present a method to construct explicitly L-infinity algebras governing simultaneous...

Journal Article

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