SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE

Abstract

The main subject of this paper is Hom-comodule algebras with

Hom-Hopf module structure. First, we give the factorization of a class of Hom-

bialgebras, which is not only Hom-module coalgebras but also Hom-comodule

algebras with Hom-Hopf module structure. Next, we obtain the factorization of

this class of Hom-comodule algebras. Finally, we discuss the relation between

this class of Hom-comodule algebas and cleft extensions.

Keywords

• Hom-comodule algebra,Hom-Hopf module,Hom-crossed product algebra,cleft extension

References

1. R. J. Blattner, M. Cohen and S. Montgomery, Crossed products and inner actions of Hopf algebras, Trans. Amer. Math. Soc., 298(2) (1986), 671-711.
2. R. J. Blattner and S. Montgomery, Crossed products and Galois extensions of Hopf algebras, Pacic J. Math., 137(1) (1989), 37-54.
3. L. H. Dong, S. Xue and X. Zhang, The factorization for a class of Hom- coalgebras, Adv. Math. Phys., (2017), 4653172 (14 pp).
4. J. T. Hartwig, D. Larsson and S. D. Silvestrov, Deformations of Lie algebras using -derivations, J. Algebra, 295(2) (2006), 314-361.
5. D. W. Lu and S. H. Wang, Crossed product Hom-Hopf algebras and lazy 2- cocycle, arXiv: 1509.01518v2.
6. T. S. Ma H. Y. Li and T. Yang, Cobraided smash product Hom-Hopf algebras, Colloq. Math., 134(1) (2014), 75-92.
7. A. Makhlouf and S. D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl., 2(2) (2008), 51-64.
8. A. Makhlouf and S. D. Silvestrov, Hom-algebras and Hom-coalgebras, J. Alge- bra Appl., 9(4) (2010), 553-589.

9. S. Montgomery, Hopf Algebras and Their Actions on Rings, CBMS Regional Conference Series in Mathematics, 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the Amer. Math. Soc., Providence, RI, 1993.
10. D. Yau, Hom-bialgebras and comodule Hom-algebras, Int. Electron. J. Algebra, 8 (2010), 45-64.