Hom-Algebras and Hom-Coalgebras
Abstract
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 involving twisted derivations and giving rise to the class of quasi-Lie algebras incorporating Hom-Lie algebras, we describe the notion and some properties of Hom-algebras and provide examples. We introduce Hom-coalgebra structures, leading to the notions of Hom-bialgebra and Hom-Hopf algebras and prove some fundamental properties and give examples. Finally, we define the concept of Hom-Lie admissible Hom-coalgebra and provide their classification based on subgroups of the symmetric group.
Keywords
Cite
@article{arxiv.0811.0400,
title = {Hom-Algebras and Hom-Coalgebras},
author = {Abdenacer Makhlouf and Sergei Silvestrov},
journal= {arXiv preprint arXiv:0811.0400},
year = {2008}
}
Comments
Published in Preprints in Mathematical Sciences, Lund University, Centre for Mathematical Sciences, Centrum Scientiarum Mathematicarum, 2008