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Title:
A topological approach to the classification of discrete amenable group actions on nuclear C* algebras
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Abstract:
A topological approach to the classification of discrete amenable group actions on nuclear C*-algebras. The classification of of discrete amenable group actions on injective factors was completed in the last century by many hands, Connes, Jones, Ocneanu, Takesaki, Kawahigashi, Sutherland, and Katayama. In contract, its C*-counterpart is still a far less developed subject though we can say that the classification of nuclear C*-algebras is a matured subject now. One reason is probably topological complication of the automorphism groups of C*-algebras, which never came into the picture in the von Neumann algebra case. In this talk, I report on our recent work with Hiroki Matui on the classification of poly-Z group G-actions on a Kirchberg algebra A. We reduce the classification problem to that of principal Aut(A)-bundles over the classifying space BG, or equivalently, to the classification problem of continuous fields of A over BG. As an application, we completely determine the number of cocycle conjugacy classes of outer Z^n-actions on the Cuntz algebras.
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