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Models of finite group actions. (English) Zbl 0551.46043
In the article the authors extend their results in the paper [J. Funct. Anal. 43, 169-176 (1982)] to finite group actions. Let A be a separable simple unital \(C^*\)-algebra. An action \(\alpha\) of a finite group G on A is said to have property \({\mathcal R}_{\infty}\) if there is a central sequence of partitions of unity \(\{e^ n_ g\}\) indexed by G such that \(\lim_{n\to \infty}\| \alpha_ g(e^ n_ h)-e^ n_{gh}\| =0.\) Then their main theorem (3.6) says that if A is further an AF- algebra isomorphic to its tensor product with a \(| G|^{\infty}\) UHF algebra B and if \(\alpha\) is an approximately inner action of G on A having property \({\mathcal R}_{\infty}\), then \(\alpha\) is conjugate to \(s_ G\otimes id\) for some factorization \(B\otimes A\), where \(s_ G\) is the infinite tensor product action of the regular representation action by conjugation on the \(| G| \times | G|\) matrix algebra.
Reviewer: J.Tomiyama

MSC:
46L55 Noncommutative dynamical systems
46L40 Automorphisms of selfadjoint operator algebras
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