Quantum algebras are a mathematical tool which provides us with a class of symmetries
wider than that of Lie algebras, which are contained in the former as a special case. After a …

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 is an introduction to non-commutative geometry, with special emphasis on those cases
where the structure algebra, which defines the geometry, is an algebra of matrices over the …

It is noted that the study of a quantum algebra su p, q (2), with two independent deformation
parameters (p, q), leads to a'(p, q)-oscillator'realization for it. The analysis is extended to the …

The structure of quantum group has appeared orig inally in the studies of the properties of
the Yang-Baxter equation [1, 2]. Subsequently, a mathemat ical formulation of quantum …

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 …