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