Inclusions of unital C^*-algebras of index-finite type with depth 2 induced by saturated actions of finite dimensional C^*-Hopf algebras - Kodaka, Kazunori; Teruya, Yamotsu (MATHEMATICA SCANDINAVICA, 2009)
Let B be a unital C^*-algebra and H a finite dimensional C^*-Hopf algebra with its dual C^*-Hopf algebra H^0. We suppose that there is a saturated action of H on B and we denote by A its fixed point C^*-subalgebra of B. Let E be the canonical conditional expectation from 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 σ of H^0 H^0 to A satisfying that there is an isomorphism π of A times_σH^0 onto B, which is the twisted crossed product of A by the weak action of H^0 on A and the unitary cocycle σ, such that F=E° π, where F is the canonical conditional expectation from A times_σH^0 onto A.