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arXiv · 0811.0400

Hom-Algebras and Hom-Coalgebras

Abdenacer Makhlouf·Sergei Silvestrov
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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.

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Abdenacer Makhlouf, Sergei Silvestrov. 2008-11-23. Hom-Algebras and Hom-Coalgebras. https://arxiv.org/abs/0811.0400

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