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.

arXiv commentPublished in Preprints in Mathematical Sciences, Lund University, Centre for Mathematical Sciences, Centrum Scientiarum Mathematicarum, 2008

References in corpus (7)

• Deformations of Lie Algebras using $\sigma$-derivations
• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Hom-bialgebras and comodule Hom-algebras
• Quasi-Deformations of sl_2(\F) using twisted derivations
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Cited by in corpus (16)

• Hom-algebras and homology
• Module Hom-algebras
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• On unitality conditions for Hom-associative algebras
• Hom-quantum groups III: Representations and module Hom-algebras
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-alternative algebras and Hom-Jordan algebras
• On Hom type algebras
• Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras
• Hom-power associative algebras
• Hom-Akivis algebras
• Extensions of hom-Lie color algebras
• Enveloping algebras of color hom-Lie algebras
• Hom-coassociative ternary coalgebras and infinitesimal bialgebras