Deformations of Lie algebras using σ-derivations
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 …
based on σ-derivations. We show that σ-twisted Jacobi type identity holds for generators of …
Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities
D Larsson, SD Silvestrov - Journal of Algebra, 2005 - Elsevier
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 …
is a natural generalization of hom-Lie algebras introduced in a previous paper [JT Hartwig …
Hom-algebras and Hom-coalgebras
A Makhlouf, S Silvestrov - Journal of Algebra and its Applications, 2010 - World Scientific
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 …
After reviewing some key constructions and examples of quasi-deformations of Lie algebras …
Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras
A Makhlouf, S Silvestrov - 2010 - degruyter.com
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 …
deformations of algebras which was introduced by Gerstenhaber for associative algebras …
BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras
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 …
commuting multiplicative linear maps $\alpha,\beta\colon A\rightarrow A $ such that $\alpha …
[HTML][HTML] Hom–Lie algebras with symmetric invariant nondegenerate bilinear forms
S Benayadi, A Makhlouf - Journal of Geometry and Physics, 2014 - Elsevier
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 …
Lie algebras equipped with symmetric invariant nondegenerate bilinear forms. We provide …
Hom-Lie superalgebras and Hom-Lie admissible superalgebras
F Ammar, A Makhlouf - Journal of algebra, 2010 - Elsevier
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 …
bracket for which the superJacobi identity is twisted by a homomorphism. This class is a …
Hom-bialgebras and comodule Hom-algebras
D Yau - International Electronic Journal of Algebra, 2010 - dergipark.org.tr
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 …
we construct a Hom-bialgebra M (2) representing the functor of 2× 2-matrices on Hom …
Generalization of n-ary Nambu algebras and beyond
H Ataguema, A Makhlouf, S Silvestrov - Journal of Mathematical …, 2009 - pubs.aip.org
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 …
algebras of Lie type including n-ary Nambu algebras, n-ary Nambu–Lie algebras and n-ary …
Hom-quantum groups: I. Quasi-triangular Hom-bialgebras
D Yau - Journal of Physics A: Mathematical and Theoretical, 2012 - iopscience.iop.org
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 …
bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi …