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- W2964082912 abstract "I combine recent results in the structure theory of nuclear ${rm C}^*$-algebras and in topological dynamics to classify certain types of crossed products in terms of their Elliott invariants. In particular, transformation group ${rm C}^*$-algebras associated to free minimal ${Bbb Z}^{d}$-actions on the Cantor set with compact space of ergodic measures are classified by their ordered ${rm K}$-theory. In fact, the respective statement holds for finite dimensional compact metrizable spaces, provided that projections of the crossed products separate tracial states. Moreover, ${rm C}^*$-algebras associated to certain minimal homeomorphisms of spheres $S^{2n+1}$ are only determined by their spaces of invariant Borel probability measures (without a condition on the space of ergodic measures). Finally, I show that for a large collection of classifiable ${rm C}^*$-algebras, crossed products by ${Bbb Z}^{d}$-actions are generically again classifiable." @default.
- W2964082912 created "2019-07-30" @default.
- W2964082912 creator A5002025468 @default.
- W2964082912 date "2016-01-01" @default.
- W2964082912 modified "2023-10-17" @default.
- W2964082912 title "Classifying crossed product C*-algebras" @default.
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- W2964082912 doi "https://doi.org/10.1353/ajm.2016.0029" @default.
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