INCLUSIONS OF UNITAL C*-ALGEBRAS OF INDEX-FINITE TYPE WITH DEPTH 2 INDUCED BY SATURATED ACTIONS OF FINITE DIMENSIONAL C*-HOPF ALGEBRAS

摘要

Let B be it unital C*-algebra and H a finite dimensional C*-Hopf algebra with its dual C*-Hopf a H-0. We Suppose that there is a saturated action of H on B and we denote by A its fixed algebra point C*-subalgebra of B. Let E be the canonical conditional expectation front B onto A. In the present paper, we shall give a necessary and sufficient condition that there are a weak action of H-0 on A and a unitary cocycle sigma of H-0 circle times H-0 to A satisfying that there is ail isomorphism pi of A x(sigma) H-0 onto B, which is the twisted crossed product of A by the weak action of H-0 on A and the unitary cocycle sigma, such that F = E circle pi, where F is the canonical conditional expectation front A x(sigma) H-0 onto A.