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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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