MORITA CONTEXT OF WEAK HOPF ALGEBRAS

Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra A~H.We prove that the smash product A#H is an A-ring with a grouplike character, and give a criterion for A#H to be Frobenius over A. Using the theory of A-rings, we mainly construct a Morita context <A~H,A#H,A,A,τ,μ> connecting the smash product A#H and the invariant subalgebra A~H , which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery.