Journal of Operator Theory
Volume 74, Issue 1, Summer 2015 pp. 3-21.
Existence of the tracial Rokhlin property
Authors:
Michael Y. Sun
Summary: We show by construction that when $G$ is an elementary
amenable group and $A$ is a unital simple nuclear and tracially
approximately divisible $C^*$-algebra, there exists an action $\omega$
of
$G$ on $A$ with the tracial Rokhlin property in the sense of Matui and
Sato. In particular, group actions with this Matui--Sato tracial
Rokhlin
property always exist for unital simple separable nuclear
$C^*$-algebras
with tracial rank at most one. If $A$ is simple with rational
tracial rank
at most one, then the crossed product $A\rtimes_{\omega}G$ is
also simple
with rational tracial rank at most one.
DOI: http://dx.doi.org/10.7900/jot.2014apr11.2031
Keywords: $C^*$-algebras, group action, tracial, Rokhlin property,
approximately divisible
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