Abstract
We give the necessary and sufficient conditions for a family of Brzezínski crossed product algebras with suitable comultiplication and counit to be a Hopf π-coalgebra. On the other hand, necessary and sufficient conditions for the Brzeziński π-crossed product A⧫H to be a coquasitriangular Hopf π-coalgebra are derived, then the category A⧫H ℳ of the left π-comodules over A⧫H is braided.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The authors are deeply indebted to the referee for his/her very useful suggestions and some improvements to the original manuscript. This work was partially supported by the NNSF of China (No. 11101128) and the NSF of Henan Province (Nos. 12A110013, 122300410110, 2011GGJS-062).
Notes
Communicated by E. Puczylowski.