Abstract
Let H be a finite-dimensional Hopf algebra and A a finite-dimensional H-simple left H-module algebra. We show that the smash product A#H is isomorphic to End A′(V ⊗ H*), where V ≠ 0 is a finite-dimensional left A-module and (A′, V′) the stabilizer of (A, V). As an application it is proved that A#H is isomorphic to a full matrix algebra over A′ when H is semisimple and dim V|dim A.
2010 Mathematic Subject Classification:
ACKNOWLEDGMENT
The authors would like to thank the referee for his/her careful reading of the paper and helpful comments.
This work is supported by National Natural Science Foundation of China (10731070 and 11126121) and Project of Science and Technology Department of Henan Province of China (102300410233).
Notes
Communicated by M. Cohen.