Hom-Algebras And Hom-Coalgebras
Makhlouf, Abdenacer; Silvestrov, Sergei (2010). Hom-Algebras And Hom-Coalgebras. Journal of Algebra and Its Applications, 9, (4), 553 - 589
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Published
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English
Authors:
Makhlouf, Abdenacer
;
Silvestrov, Sergei
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Research Group:
Non-commutative Geometry-lup-obsolete
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:
Hom-Lie algebra ;
Hom-coalgebra ;
Hom-bialgebra ;
Hom-Lie admissible Hom-coalgebra ;
Hom-Hopf algebra ;
Hom-associative algebra
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