Related papers: Split extensions of BiHom-Lie algebras
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
The aim of this paper is to explore non-abelian extensions of Bol algebras and to study the extensibility of a pair of automorphisms within these non-abelian extensions. We begin by researching non-abelian extensions of Bol algebras and…
In this paper, we explore non-abelian extensions of relative Rota-Baxter Lie algebras and classify the non-abelian extensions by introducing the non-abelian second cohomology group. We also study the inducibility of a pair of automorphisms…
BiHom-Akivis algebras are introduced. The BiHom-commutator-BiHom-associator algebra of a regular BiHom-algebra is a BiHom-Akivis algebra. It is shown that BiHom-Akivis algebras can be obtained from Akivis algebras by twisting along two…
We survey decades of research identifying the (co)homology of configuration spaces with Lie algebra (co)homology. The different routes to this one proto-theorem offer genuinely different explanations of its truth, and we attempt to convey…
We present the results of computation of cohomology for some Lie (super)algebras of Hamiltonian vector fields and related algebras. At present, the full cohomology rings for these algebras are not known even for the low dimensional vector…
The aim of this paper is to develop the theory of Hom-coalgebras and related structures. After reviewing some key constructions and examples of quasi-deformations of Lie algebras involving twisted derivations and giving rise to the class of…
In this paper, we introduce the concepts of crossed modules of post-Lie algebras and cat$^1$-post-Lie algebras. It is proved that these two concepts are equivalent to each other. Secondly, we construct a non-abelian cohomology for post-Lie…
In this paper, we give Maurer-Cartan characterizations as well as a cohomology theory for compatible Lie algebras. Explicitly, we first introduce the notion of a bidifferential graded Lie algebra and thus give Maurer-Cartan…
In this paper, we investigate non-abelian extensions of Lie algebras with derivations using several different approaches. We show that the theory of non-abelian extensions of a Lie algebra with a derivation can be characterized by means of…
This note presents a general theorem about the cohomology of finite dimensional Lie algebras of arbitrary characteristic. As an application we compute the cohomology of the Borel subalgebra of sl(N).
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…
Let $V$ be a vertex algebra and $M$ a $V$-module. We define the first and second cohomology of $V$ with coefficients in $M$, and we show that the second cohomology $H^{2}(V, M)$ corresponds bijectively to the set of equivalence classes of…
We introduce a notion of $n$-Lie Rinehart algebras as a generalization of Lie Rinehart algebras to $n$-ary case. This notion is also an algebraic analogue of $n$-Lie algebroids. We develop representation theory and describe a cohomology…
In this paper, we introduce the concept and representation of modified $\lambda$-differential Lie triple systems. Next, we define the cohomology of modified $\lambda$-differential Lie triple systems with coefficients in a suitable…
In this paper, we develop a cohomology theory of a left-symmetric conformal algebra and study its some applications. We define the cohomology of a left-symmetric conformal algebra, and then give an isomorphism between the cohomology spaces…
We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme (X,O), and a sheaf of finitely generated Lie O-algebras L, we determine the obstruction to the existence of…
This paper introduces the concept of representations for Com-PreLie algebras and develops corresponding cohomology theories, examining how cohomology groups can be applied in the context of Com-PreLie algebras. Initially, we utilize the…
Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic…
Motivated by the classical correspondence between short exact sequences and splitting properties in module theory, this paper examines the projective and injective analogues within the category of Lie algebras. We first show that no Lie…