Related papers: Restricted simple Lie algebras and their infinites…
Let $L$ be a restricted Lie algebra over a field of characteristic $p>2$ and denote by $u(L)$ its restricted enveloping algebra. We establish when the symmetric or skew elements of $u(L)$ under the principal involution are Lie metabelian.
In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras.…
We consider deformations of finite or infinite dimensional Lie algebras over a field of characteristic 0. There is substantial confusion in the literature if one tries to describe all the non-equivalent deformations of a given Lie algebra.…
We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…
We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…
The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base.…
In this paper, we consider deformations of Lie 2-algebras via the cohomology theory. We prove that a 1-parameter infinitesimal deformation of a Lie 2-algebra $\g$ corresponds to a 2-cocycle of $\g$ with the coefficients in the adjoint…
This paper mainly studies the ResLieDer pair in characteristic 2, that is, a restricted Lie algebra with a restricted derivation. We define the restricted representation of a ResLieDer pair and the corresponding cohomology complex. We show…
We study the problem of the infinitesimal deformations of all real, simple, finite-dimensional Filippov (or n-Lie) algebras, considered as a class of n-Leibniz algebras characterized by having an n-bracket skewsymmetric in its n-1 first…
We study the space of Lie algebras equipped with left-invariant complex structures, $\mathcal{L}_{ J_{\tiny{\mbox{cn}}} }(\mathbb{R}^{2n}) $, with particular attention to their degenerations and deformations. To this end, we identify…
We consider degenerations of all simple Lie algebras of exceptional type obtained by embedding into affine Lie algebras. We give a filtration to consider this as an abelianisation of the original Lie algebra. We then show that the…
In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of…
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
Restricted twisted Heisenberg Lie superalgebras are studied over an algebraically closed field F of characteristic p > 0. We determine the restricted structures and use the ordinary 1- and 2-cohomology spaces with trivial coefficients to…
In this paper we will study deformations of A-infinity algebras. We will also answer questions relating to Moore algebras which are one of the simplest nontrivial examples of an A-infinity algebra. We will compute the Hochschild cohomology…
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
A cohomology theory of weighted Rota-Baxter $3$-Lie algebras is introduced. Formal deformations, abelian extensions, skeletal weighted Rota-Baxter $3$-Lie 2-algebras and crossed modules of weighted Rota-Baxter 3-Lie algebras are interpreted…
We apply the notion of 2-extensions of algebras to the deformation theory of algebras. After standard results on butterflies between 2-extensions, we use this (2, 0)-category to give three perspectives on the deformation theory of algebras.…
We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…
Lie solvable restricted enveloping algebras were characterized by Riley and Shalev except when the ground field is of characteristic 2. We resolve the characteristic 2 case here which completes the classification. As an application of our…