Group Entwining Structures and Group Coalgebra Galois Extensions

Abstract

The notions of group coalgebra Galois extension and group entwining structure are defined. It is proved that any group coalgebra Galois extension induces a unique group-entwining map ψ = {ψ_{α, β}}_{α, β∈π} compatible with the right group coaction, generalizing the recent work of Brzeziński and Hajac [Brzeziński, T., Hajac, P. M. (1999). Coalgebra extensions and algebra coextensions of Galois type. Comm. Algebra 27:1347–1368].

Key Words:

• Group entwining
• Doi–Hopf group module
• Group coalgebra Galois extension

Mathematical Subject Classification:

• 16W30
• 16W50

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.