AN IMPRIMITIVITY THEOREM FOR FINITE ALGEBRAIC QUANTUM GROUPS

Let G be an algebraic quantum group and U a compact quantum subgroup. Given a left Uˆ-module algebra A with unit, we can endow A ⊗ G with a structure of a right Uˆ-module algebra. The algebra of invariants for this action (A ⊗ G) Uˆ has a left action of Gˆ. We prove that for finite G, (A ⊗ G) Uˆ#Gˆ is Morita equivalent to A#Uˆ.