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 [Citation8] to the setting of Hopf π-coalgebras.
2010 Mathematics Subject Classification:
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.