A GENERALIZED POWERS AVERAGING PROPERTY FOR COMMUTATIVE CROSSED PRODUCTS

Tattwamasi Amrutam, Dan Ursu

Research output: Contribution to journalArticlepeer-review

Abstract

We prove a generalized version of Powers’ averaging property that characterizes simplicity of reduced crossed products C(X) λ 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) λ G and to Kawabe’s generalized space of amenable subgroups Suba(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 ) ⊆ C(X) is an inclusion of unital commutative G-C*-algebras with X minimal and C(Y )λG simple, then any intermediate C*-algebra A satisfying C(Y ) λ G ⊆ A ⊆ C(X) λ G is simple.

Original languageEnglish
Pages (from-to)2237-2254
Number of pages18
JournalTransactions of the American Mathematical Society
Volume375
Issue number3
DOIs
StatePublished - 1 Jan 2022

Keywords

  • C*-algebra
  • Compact space
  • Crossed product
  • Group action
  • Minimal
  • Powers averaging property
  • Simple

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