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Stable rank for crossed products by actions of finite groups on C*-algebras
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abstract
Let $G$ be a finite group, $A$ a unital separable finite simple nuclear C*-algebra, and $\alpha$ an action of $G$ on $A$. Assume that $A$ absorbs the Jiang-Su algebra $\mathcal{Z}$, the extremal boundary of the trace space of $A$ is compact and finite dimensional and that $\alpha$ fixes any tracial state of $A$. Then tsr$(A \rtimes_\alpha G) = 1$. In particular, when $A$ has a unique tracial state, we conclude it without above conditons on a tracial state space of $A$.
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The Cuntz semigroup and the radius of comparison of the crossed product by a finite group
For finite group actions with the weak tracial Rokhlin property on simple stably finite C*-algebras, the fixed point algebra has radius of comparison at most that of A, and the crossed product at most one over the gro...
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