Finite group actions with the weak tracial Rokhlin property and compact group actions with the tracial Rokhlin property with comparison preserve uniform property Gamma in crossed products and fixed-point algebras.
Stable rank for crossed products by finite group actions with the weak tracial Rokhlin property
1 Pith paper cite this work. Polarity classification is still indexing.
abstract
Let $A$ be an infinite-dimensional stably finite simple unital C*-algebra, let $G$ be a finite group, and let $\alpha\colon G\rightarrow \mathrm{Aut}(A)$ be an action of $G$ on $A$ which has the weak tracial Rokhlin property. We prove that if $A$ has property (TM), then the crossed product $A\rtimes_\alpha G$ has property (TM). As a corollary, if $A$ is an infinite-dimensional separable simple unital C*-algebra which has stable rank one and strict comparison, $\alpha\colon G\rightarrow \mathrm{Aut}(A)$ is an action of a finite group $G$ on $A$ with the weak tracial Rokhlin property, then $A\rtimes_\alpha G$ has stable rank one.
citation-role summary
citation-polarity summary
fields
math.OA 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Uniform property $\Gamma$ for Crossed products by group actions with the Rokhlin-type properties
Finite group actions with the weak tracial Rokhlin property and compact group actions with the tracial Rokhlin property with comparison preserve uniform property Gamma in crossed products and fixed-point algebras.