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arXiv · 1205.1590

Z-stability of crossed products by strongly outer actions II

Hiroki Matui·Yasuhiko Sato
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Abstract

We consider a crossed product of a unital simple separable nuclear stably finite Z-stable C*-algebra A by a strongly outer cocycle action of a discrete countable amenable group \Gamma. Under the assumption that A has finitely many extremal tracial states and \Gamma is elementary amenable, we show that the twisted crossed product C*-algebra is Z-stable. As an application, we also prove that all strongly outer cocycle actions of the Klein bottle group on Z are cocycle conjugate to each other. This is the first classification result for actions of non-abelian infinite groups on stably finite C*-algebras.

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Hiroki Matui, Yasuhiko Sato. 2012-05-08. Z-stability of crossed products by strongly outer actions II. https://doi.org/10.1007/s00220-011-1392-9

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