In this article we develop an approach to deformations of the Witt and Virasoro algebras
based on σ-derivations. We show that σ-twisted Jacobi type identity holds for generators of …

This paper introduces the notion of a quasi-hom-Lie algebra, or simply, a qhl-algebra, which
is a natural generalization of hom-Lie algebras introduced in a previous paper [JT Hartwig …

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 …

The aim of this paper is to extend to Hom-algebra structures the theory of 1-parameter formal
deformations of algebras which was introduced by Gerstenhaber for associative algebras …

A BiHom-associative algebra is a (nonassociative) algebra $ A $ endowed with two
commuting multiplicative linear maps $\alpha,\beta\colon A\rightarrow A $ such that $\alpha …

The aim of this paper is to introduce and study quadratic Hom–Lie algebras, which are Hom–
Lie algebras equipped with symmetric invariant nondegenerate bilinear forms. We provide …

The purpose of this paper is to study Hom-Lie superalgebras, that is a superspace with a
bracket for which the superJacobi identity is twisted by a homomorphism. This class is a …

We study Hom-bialgebras and objects admitting coactions by Hom-bialgebras. In particular,
we construct a Hom-bialgebra M (2) representing the functor of 2× 2-matrices on Hom …

The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary
algebras of Lie type including n-ary Nambu algebras, n-ary Nambu–Lie algebras and n-ary …

We introduce a twisted generalization of quantum groups, called quasi-triangular Hom-
bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi …