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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Topological Invariants for G-kernels and Group Actions
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If you have a question about this talk, please contact nobody. QIAW02 - New trends at the intersection of quantum information theory, quantum groups and operator algebras A G -kernel is a group homomorphism from a (discrete) group G to Out(A), the outer automorphism group of a C-algebra A. There are cohomological obstructions to lifting such a G-kernel to a group action. In the setting of von Neumann algebras, G-kernels on the hyperfinite II1 -factor have been completely understood via deep results of Connes, Jones and Ocneanu. In the talk I will explain how G-kernels on C-algebras and the lifting obstructions can be interpreted in terms cohomology with coefficients in crossed modules. G-kernels, group actions and cocycle actions then give rise to induced maps on classifying spaces. For strongly self-absorbing C*-algebras these classifying spaces turn out to be infinite loop spaces creating a bridge to stable homotopy theory. Not only does this make the invariants computable, it also gives rise to equivariant refinements. The first part is a joint project with S. Giron Pacheco and M. Izumi, the second with my PhD student V. Bianchi. This talk is part of the Isaac Newton Institute Seminar Series series. This talk is included in these lists:
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