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

  • Abdenacer MakhloufEmail author
  • Sergei SilvestrovEmail author

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 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques, Informatique et ApplicationsUniversité de Haute AlsaceMulhouseFrance

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