On Twisted Smash Products of Monoidal Hom–Hopf Algebras

Abstract

Let (H, α) be a monoidal Hom-Hopf algebra and (A, β) be an (H, α)-Hom-bimodule algebra. In this article, we first introduce the notion of a twisted Hom-smash product A☆H and then find some sufficient and necessary conditions making it into a monoidal Hom-bialgebra. Furthermore, we give a Maschke-type theorem for the twisted Hom-smash product over a semisimple monoidal Hom-Hopf algebra (H, α). Finally, we form an associated Morita context [A^biH, _A^biHA_A☆H, _A☆HA_A^biH, A☆H] in the category .

Key Words:

• Monoidal Hom-Hopf algebra
• Maschke-type theorem
• Morita context
• Twisted Hom-smash product

2010 Mathematics Subject Classification:

• 16S40

ACKNOWLEDGMENTS

The authors sincerely thank the referee for his or her valuable suggestions and comments on this article.