Abstract
The notions of Doi–Hopf group module and group twisted smash product are defined as a respective generalization of an ordinary Doi–Hopf module and a usual twisted smash product. It is shown that the Zunino's Yetter-Drinfel'd modules are special cases as these new Doi–Hopf group modules and that the Zunino's Drinfel'd double appears as a type of such a group twisted smash product, respectively. Furthermore, the concepts of group skew pair and generalized group smash product are introduced. As for a group skew pair σ for a T- coalgebra H and a T-algebra B, it is proved that a group twisted smash product is a Hopf group coalgebra if H has a bijective antipode, and that is a special case of such a generalized group smash product.
Acknowledgments
The author would like to thank the referee for his/her helpful comments on this paper. This work was supported in part by the Science Foundation of Henan Province for Distinguished Young Scholars and the NSF of China.
Notes
#Communicated by M. Cohen.