Inclusions of unital C∗-algebras of index-finite type with depth 2 induced by saturated actions of finite dimensional C∗-Hopf algebras
DOI:
https://doi.org/10.7146/math.scand.a-15096Abstract
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⋊ 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\circ \pi, where F is the canonical conditional expectation from A\rtimes_{\sigma}H^0 onto A.Downloads
Published
2009-06-01
How to Cite
Kodaka, K., & Teruya, Y. (2009). Inclusions of unital C^*-algebras of index-finite type with depth 2 induced by saturated actions of finite dimensional C^*-Hopf algebras. MATHEMATICA SCANDINAVICA, 104(2), 221–248. https://doi.org/10.7146/math.scand.a-15096
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