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A generalized Powers averaging property for commutative crossed products.
- Source :
-
Transactions of the American Mathematical Society . Mar2022, Vol. 375 Issue 3, p2237-2254. 18p. - Publication Year :
- 2022
-
Abstract
- We prove a generalized version of Powers' averaging property that characterizes simplicity of reduced crossed products C(X) \rtimes _\lambda G, where G is a countable discrete group, and X is a compact Hausdorff space which G acts on minimally by homeomorphisms. As a consequence, we generalize results of Hartman and Kalantar on unique stationarity to the state space of C(X) \rtimes _\lambda G and to Kawabe's generalized space of amenable subgroups \operatorname {Sub}_a(X,G). This further lets us generalize a result of the first named author and Kalantar on simplicity of intermediate C*-algebras. We prove that if C(Y) \subseteq C(X) is an inclusion of unital commutative G-C*-algebras with X minimal and C(Y) \rtimes _\lambda G simple, then any intermediate C*-algebra A satisfying C(Y) \rtimes _\lambda G \subseteq A \subseteq C(X) \rtimes _\lambda G is simple. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 375
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 155859577
- Full Text :
- https://doi.org/10.1090/tran/8567