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- Title
The Cuntz semigroup and the radius of comparison of the crossed product by a finite group.
- Authors
ASADI-VASFI, M. ALI; GOLESTANI, NASSER; PHILLIPS, N. CHRISTOPHER
- Abstract
Let G be a finite group, let A be an infinite-dimensional stably finite simple unital C*-algebra, and let α : G → Aut(A) be an action of G on A which has the weak tracial Rokhlin property. Let Aα be the fixed point algebra. Then the radius of comparison satisfies rc(Aα) ≤ rc(A) and rc(C* (G, A, α)) ≤ (1/card(G)) ⋅ rc(A). The inclusion of Aα in A induces an isomorphism from the purely positive part of the Cuntz semigroup Cu(Aα) to the fixed points of the purely positive part of Cu(A), and the purely positive part of Cu(C*(G, A, α)) is isomorphic to this semigroup. We construct an example in which G = Z/ 2Z, A is a simple unital AH algebra, α has the Rokhlin property, rc(A) > 0 , rc(Aα) = rc(A), and rc(C* (G, A, α)) = (1/2) rc(A).
- Publication
Ergodic Theory & Dynamical Systems, 2021, Vol 41, Issue 12, p3541
- ISSN
0143-3857
- Publication type
Article
- DOI
10.1017/etds.2020.121