Hom-Lie Admissible Hom-Coalgebras and Hom-Hopf Algebras

Abdenacer Makhlouf () and Sergei Silvestrov ()
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Abdenacer Makhlouf: Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications
Sergei Silvestrov: Lund Institute of Technology, Lund University, Centre for Mathematical Sciences, Division of Mathematics

Chapter 17 in Generalized Lie Theory in Mathematics, Physics and Beyond, 2009, pp 189-206 from Springer

Abstract: The aim of this paper is to develop the coalgebra counterpart of the notions introduced by the authors in a previous paper, we introduce the notions of Hom-coalgebra, Hom-coassociative coalgebra and G-Hom-coalgebra for any subgroup G of permutation group S script>3. Also we extend the concept of Lie-admissible coalgebra by Goze and Remm to Hom-coalgebras and show that G-Hom-coalgebras are Hom-Lie admissible Hom-coalgebras, and also establish duality correspondence between classes of G-Hom-coalgebras and G-Hom-algebras. In another hand, we provide relevant definitions and basic properties of Hom-Hopf algebras generalizing the classical Hopf algebras and define the module and comodule structure over Hom-associative algebra or Hom-coassociative coalgebra.

Keywords: Symmetric Group; Associative Algebra; Permutation Group; Primitive Element; Convolution Product (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-85332-9_17

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DOI: 10.1007/978-3-540-85332-9_17

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