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The Cuntz semigroup and the radius of comparison of the crossed product by a finite group by M. ALI ASADI-VASFI; NASSER GOLESTANI; N. CHRISTOPHER PHILLIPS is a Mathematics article available to read on EtoBox.

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## Abstract LetGbe a finite group, letAbe an infinite-dimensional stably finite simple unital C\*-algebra, and let$\alpha \colon G \to {\operatorname {Aut}} (A)$be an action ofGonAwhich has the weak tracial Rokhlin property. Let$A^{\alpha }$be the fixed point algebra. Then the radius of comparison satisfies${\operatorname {rc}} (A^{\alpha }) \leq {\operatorname {rc}} (A)$and${\operatorname {rc}} ( C^\* (G, A, \alpha ) ) \leq ({1}/{{{\operatorname{card}}} (G))} \cdot {\operatorname {rc}} (A)$. The inclusion of$A^{\alpha }$inAinduces an isomorphism from the purely positive part of the Cuntz semigroup${\operatorname {Cu}} (A^{\alpha })$to the fixed points of the purely positive part of${\operatorname {Cu}} (A)$, and the purely positive part of${\operatorname {Cu}} ( C^\* (G, A, \alpha ) )$is isomorphic to this semigroup. We construct an example in which$G \,{=}\, {\mathbb {Z}} / 2 {\mathbb {Z}}$,Ais a simple unital AH algebra,$\alpha $has the Rokhlin property,${\operatorname {rc}} (A)> 0$,${\operatorname {rc}} (A^{\alpha }) = {\operatorname {rc}} (A)$, and${\operatorname {rc}} ({C^\* (G, A, \alpha)} ) = ({1}/{2}) {\operatorname {rc}} (A)$.

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Author

M. ALI ASADI-VASFI; NASSER GOLESTANI; N. CHRISTOPHER PHILLIPS

Publisher

Cambridge University Press (CUP)

Published

2021

Language

EN

Field

Mathematics (Physical Sciences)