Ƶ-stability of crossed products by strongly outer actions II

Hiroki Matui, Yasuhiko Sato

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

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

Original languageEnglish
Pages (from-to)1441-1496
Number of pages56
JournalAmerican Journal of Mathematics
Volume136
Issue number6
DOIs
Publication statusPublished - Dec 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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