A Morita Context and Galois Extensions for Quasi-Hopf Algebras

Abstract

If H is a finite dimensional quasi-Hopf algebra and A is a left H-module algebra, we show that there is a Morita context connecting the smash product A#H and the subalgebra of invariants A ^H . We define also Galois extensions and prove the connection with this Morita context, as in the Hopf case.

Key Words:

• Galois extension
• Morita context
• Quasi-Hoff algebra
• Smash product

2000 Mathematics Subject Classification:

• 16W30

ACKNOWLEDGMENT

The author would like to thank C. Năstăsescu, F. Panaite, and D. Bulacu for their useful comments which improved this article.

Notes

Communicated by R. Wisbauer.