2019/08/17 by M. Ali Asadi-Vasfi, Asadi-Vasfi, M. Ali, Nasser Golestani +3 · 4 citations
Mathematics · #19K14 #46L55 (primary) #46L80 (secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1908.06343
openalex publication_date 2019/08/17 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Let G be a finite group, let A be an infinite-dimensional stably finite\nsimple unital C*-algebra, and let \α colon G \→ Aut (A) be an action of G\non A which has the weak tracial Rokhlin property. Let A\α be the fixed\npoint algebra. Then the radius of comparison satisfies rc (A\α) \≤ rc\n(A) and rc ( C* (G, A, \α) ) \≤ ( 1 / card (G) ) rc (A). The inclusion of\nA\α in A induces an isomorphism from the purely positive part of the\nCuntz semigroup Cu (A\α) to the fixed points of the purely positive part\nof Cu (A), and the purely positive part of Cu ( C* (G, A, \α) ) is\nisomorphic to this semigroup. We construct an example in which G is the two\nelement group, A is a simple unital AH algebra, \α has the Rokhlin\nproperty, rc (A) > 0, rc (A\α) = rc (A), and rc (C* (G, A, \α)) =\n(1/2) rc (A).\n