Smash Products and π-H-Comodules of Linear Maps for HOPF π-Comodules

Abstract

With an aim to explore homological algebra for Hopf π-coalgebras, this article investigates the HOM-functor and presents the structure theorem for endomorphism algebras of two-sided π--Hopf modules, where is a Hopf π-coalgebra and is a right π--comodule algebra. Moreover, we give a duality theorem involving endomorphism rings of -Hopf modules, “big” smash product and the smash product, where is a cofree Hopf π-coalgebra and A is a right -comodule algebra. Finally, under the condition “π--Galois extensions,” we generalize Theorem 2.5 of Menini and Raianu [8] to the setting of Hopf π-coalgebras.

Key Words:

• Hopf π-coalgebra
• ( H , A)-Hopf module
• π-( H , A)-Hopf module
• π- H -Galois extension

2010 Mathematics Subject Classification:

• 16W30

ACKNOWLEDGMENTS

The authors would like to thank the referee for his/her constructive comments, and they are grateful for Professor Miriam Cohen's fruitful conversations.

Notes

Communicated by M. Cohen.