Hom-Lie Admissible Hom-Coalgebras and Hom-Hopf Algebras
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.
KeywordsSymmetric Group Associative Algebra Permutation Group Primitive Element Convolution Product
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- 1.Drinfel'd V. G.: Hopf algebras and the quantum Yang—Baxter equation, Soviet Math. Doklady 32, 254–258 (1985)Google Scholar
- 6.Kassel C.: Quantum groups, Graduate Text in Mathematics, Springer, Berlin (1995)Google Scholar
- 13.Montgomery S.: Hopf algebras and their actions on rings, AMS Regional Conference Series in Mathematics 82, (1993)Google Scholar