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Lie. varvalis / varvelis
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Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Given a (quasi-)twilled pre-Lie algebra, we first construct a differential graded Lie algebra ([Formula: see text]-algebra). Then we study the twisting theory of (quasi-)twilled pr...
Deformations and abelian extensions of compatible pre-Lie superalgebras
Deformations and abelian extensions of compatible pre-Lie superalgebras
In this paper, we give cohomologies and deformations theory, as well as abelian extensions for compatible pre-Lie superalgebras. Explicitly, we first introduce the notation of a co...
Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Th...
Categorification of $ \mathsf{VB} $-Lie algebroids and $ \mathsf{VB} $-Courant algebroids
Categorification of $ \mathsf{VB} $-Lie algebroids and $ \mathsf{VB} $-Courant algebroids
<abstract><p>In this paper, first we introduce the notion of a $ \mathsf{VB} $-Lie $ 2 $-algebroid, which can be viewed as the categorification of a $ \mathsf{VB} $-L...
LIE -HIGHER DERIVATIONS AND LIE -HIGHER DERIVABLE MAPPINGS
LIE -HIGHER DERIVATIONS AND LIE -HIGHER DERIVABLE MAPPINGS
Let ${\mathcal{A}}$ be a unital torsion-free algebra over a unital commutative ring ${\mathcal{R}}$. To characterise Lie $n$-higher derivations on ${\mathcal{A}}$, we give an ident...
Étude et déformations des (super)algèbres de Lie-Rinehart en caractéristique positive
Étude et déformations des (super)algèbres de Lie-Rinehart en caractéristique positive
L'objectif de cette thèse est l'étude des algèbres de Lie-Rinehart, en particulier en caractéristique positive. On s'intéresse à leur structure, leur cohomologie, leurs déformation...
Mock-Lie bialgebras and mock-Lie analogue of the classical Yang-Baxter equation
Mock-Lie bialgebras and mock-Lie analogue of the classical Yang-Baxter equation
Abstract
The aim of this paper is to introduce the notion of a mock-Lie bialgebra which is equivalent to a Manin triple of mock-Lie algebras. The study of a special case ca...
3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras
3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras
In this paper, we first introduce the notion of a 3-Hom–Lie bialgebra and give an equivalent description of the 3-Hom–Lie bialgebras, the matched pairs and the Manin triples of 3-H...