Weakly tracially approximately representable actions
Abstract
We describe a weak tracial analog of approximate representability under the name "weak tracial approximate representability" for finite group actions. Let $G$ be a finite abelian group, let $A$ be an infinite-dimensional simple unital C*-algebra, and let $\alpha \colon G \to \operatorname{Aut} (A)$ be an action of $G$ on $A$ which is pointwise outer. Then $\alpha$ has the weak tracial Rokhlin property if and only if the dual action $\widehat{\alpha}$ of the Pontryagin dual $\widehat{G}$ on the crossed product $C^*(G, A, \alpha)$ is weakly tracially approximately representable, and $\alpha$ is weakly tracially approximately representable if and only if the dual action $\widehat{\alpha}$ has the weak tracial Rokhlin property. This generalizes the results of Izumi in 2004 and Phillips in 2011 on the dual actions of finite abelian groups on unital simple C*-algebras.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2021
- DOI:
- 10.48550/arXiv.2110.07081
- arXiv:
- arXiv:2110.07081
- Bibcode:
- 2021arXiv211007081A
- Keywords:
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- Mathematics - Operator Algebras;
- Mathematics - Functional Analysis;
- 46L55;
- 19K14;
- 46L80
- E-Print:
- 20 pages, J. Operator Theory, to appear