相关论文: On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map. We develop…
Results about the following classes of finite-dimensional Lie algebras over a field of characteristic zero are presented: anisotropic (i.e., Lie algebras for which each adjoint operator is semisimple), regular (i.e., Lie algebras in which…
In this work we give an inductive way to construct quadratic Hom-Lie algebras with twist maps in the centroid. We focus on those Hom-Lie algebras which are not Lie algebras. We prove that a Hom-Lie algebra of this type has trivial center…
The main goal of this paper is to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, $\alpha^k$-derivations and provide a classification in low dimension. We…
The purpose of this paper is to study hom-algebroids, among them left symmetric hom-algebroids and symplectic hom-algebroids by providing some characterizations and geometric interpretations. Therefore, we introduce and study…
In this article, we use the theory of (non-abelian) exterior product of Hom-Lie algebras to prove the Hopf formula for these algebras. As an application, we construct an eight-term sequence in the homology of Hom-Lie algebras. We also…
We construct explicitly groups associated to specific ternary algebras which extend the Lie (super)algebras (called Lie algebras of order three). It turns out that the natural variables which appear in this construction are variables which…
In this paper some characterizations of Hom-Leibniz superalgebras are given and some of their basic properties are found. These properties can be seen as a generalization of corresponding well-known properties of Hom-Leibniz algebras.…
A Nijenhuis mock-Lie algebra is a mock-Lie algebra equipped with a Nijenhuis operator. The purpose of this paper is to extend the well-known results about Nijenhuis mock-Lie algebras to the realm of mock-Lie bialgebras. It aims to…
Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple…
In this paper, we first introduce the notion of a weighted $\mathcal{O}$-operator on Hom-Lie triple systems with respect to an action on another Hom-Lie triple system. Next, we construct a cohomology of weighted $\mathcal{O}$-operator on…
In this paper, we introduced the notion of Hom-Lie antialgebras. The representations and cohomology theory of Hom-Lie antialgebras are investigated. We prove that the equivalent classes of abelian extensions of Hom-Lie antialgebras are in…
The representation and cohomology theory of Hom-Lie-Yamaguti algebras is introduced. As an application, we study deformation and extension of Hom-Lie-Yamaguti algebras. It proved that a 1-parameter infinitesimal deformation of a…
The purpose of this paper is to give a general survey of Hom-bialgebras, which are bialgebra-type structures where the identities are twisted by a morphism, and to extend the concept of quasi-bialgebra to Hom-setting. We provide some key…
The purpose of this paper is to provide new constructions of Hom-associative algebras using Hom-analogues of certain operators called twistors and pseudotwistors, by deforming a given Hom-associative multiplication into a new…
In this article we will build a universal imbedding of a regular Hom- Lie triple system into a Lie algebra and show that the category of regular Hom-Lie triple systems is equivalent to a full subcategory of pairs of…
In this paper, we introduce a new definition of a hom-Lie bialgebra, which is equivalent to a Manin triple of hom-Lie algebras. We also introduce a notion of an $\mathcal O$-operator and then construct solutions of the classical…
There are three kinds of Lie superalgebras for each differentiable manifold. In this note, we shall show an application of the homology groups of those superalgebras in order to classify 4 dimensional Engel-like Lie algebras.
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…
A Hom-group G is a nonassociative version of a group where associativity, invertibility, and unitality are twisted by a map \alpha: G\longrightarrow G. Introducing the Hom-group algebra KG, we observe that Hom-groups are providing examples…