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

In: Generalized Lie Theory in Mathematics, Physics and Beyond

Author

Listed:
  • 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)

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.

Suggested Citation

  • Abdenacer Makhlouf & Sergei Silvestrov, 2009. "Hom-Lie Admissible Hom-Coalgebras and Hom-Hopf Algebras," Springer Books, in: Sergei Silvestrov & Eugen Paal & Viktor Abramov & Alexander Stolin (ed.), Generalized Lie Theory in Mathematics, Physics and Beyond, chapter 17, pages 189-206, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-85332-9_17
    DOI: 10.1007/978-3-540-85332-9_17
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