Inclusions of unital C*-algebras of index-finite type with depth 2 induced by saturated actions of finite dimensional C*-Hopf algebras

• Autores: Kazunori Kodaka, Yamotsu Teruya
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 104, Nº 2, 2009, págs. 221-248
• Idioma: inglés
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• Resumen

  • Let B be a unital C∗-algebra and H a finite dimensional C∗-Hopf algebra with its dual C∗-Hopf algebra H0. 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 H0 on A and a unitary cocycle σ of H0⊗H0 to A satisfying that there is an isomorphism π of A⋊σH0 onto B, which is the twisted crossed product of A by the weak action of H0 on A and the unitary cocycle σ, such that F=E∘π, where F is the canonical conditional expectation from A⋊σH0 onto A.