相关论文: Cohomologies and deformations of right-symmetric a…
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 introduce a notion of left-symmetric Rinehart algebras, which is a generalization of a left-symmetric algebras. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie-Rinehart algebra. We construct…
An algebra $A$ with multiplication $A\times A \to A, (a,b)\mapsto a\circ b$, is called right-symmetric, if $a\circ(b\circ c)-(a\circ b)\circ a\circ (c\circ b)-(a\circ c)\circ b,$ for any $a,b,c\in A$. The multiplication of right-symmetric…
The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.
The purpose of this paper is to develop a cohomology and deformation theories for generalized left-symmetric algebras.We introduce the notions of generalized left-symmetric cohomology and deformation. We also generalize a theorem 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…
In this paper, we define the cohomology of a modified Rota-Baxter Leibniz algebra with coefficients in a suitable representation. As applications of our cohomology, we study formal one-parameter deformations and abelian extensions of…
We study formal deformations of hom-Lie-Rinehart algebras. The associated deformation cohomology that controls deformations is constructed using multiderivations of hom-Lie-Rinehart algebras.
A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be…
A Rota-Baxter Leibniz algebra is a Leibniz algebra $(\mathfrak{g},[~,~]_{\mathfrak{g}})$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. We define representation and dual representation of Rota-Baxter…
An algebra is called skew-symmetric if its multiplication operation is a skew-symmetric bilinear application. We determine all these algebras in dimension $3$ over a field of characteristic different from $2$. As an application, we…
Classes of $G$-Hom-associative algebras are constructed as deformations of $G$-associative algebras along algebra endomorphisms. As special cases, we obtain Hom-associative and Hom-Lie algebras as deformations of associative and Lie…
A structure of a left-symmetric algebra on the set of all derivations of a free algebra is introduced such that its commutator algebra becomes the usual Lie algebra of derivations. Left and right nilpotent elements of left-symmetric…
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.
In this paper, we introduce a notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding…
In this paper, we introduce cohomology of n-Hom-Liebniz algebra morphisms and formal deformation theory of n-Hom-Liebniz algebra morphisms .
This paper begins by introducing the concept of a quasi-hom-Lie algebra which is a natural generalization of hom-Lie algebras introduced in a previous paper by the authors. Quasi-hom-Lie algebras include also as special cases (color) Lie…
The aim of this work is to introduce representations of BiHom-left-symmetric algebras. and develop its cohomology theory. As applications, we study linear deformations of BiHom-left-symmetric algebras, which are characterized by its second…
In this paper we define a new cohomology theory for a $B$-algebra $A$. We use this cohomology to study deformations of algebras $A[[t]]$, that have a $B$-algebra structure.
The aim of this paper is to deal with BiHom-alternative algebras which are a generalization of alternative and Hom-alternative algebras, their structure is defined with two commuting multiplicative linear maps. We study cohomology and…