The radius of comparison of the crossed product by a weakly tracially strictly approximately inner action

0582728 - MÚ 2024 RIV PL eng J - Journal Article
Asadi-Vasfi, M. Ali
The radius of comparison of the crossed product by a weakly tracially strictly approximately inner action.
Studia mathematica. Roč. 271, č. 3 (2023), s. 241-285. ISSN 0039-3223. E-ISSN 1730-6337
R&D Projects: GA ČR(CZ) GJ20-17488Y
Institutional support: RVO:67985840
Keywords : C∗-algebras * C∗-dynamical systems * radius of comparison
OECD category: Pure mathematics
Impact factor: 0.8, year: 2022
Method of publishing: Limited access
https://doi.org/10.4064/sm211002-5-4

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 a weakly tracially strictly approximately inner action of G on A. Then the radius of comparison satisfies rc(A) ≤ rc(C∗(G, A, α)), and if C∗(G, A, α) is simple, then rc(A) ≤ rc(C∗(G, A, α)) ≤ rc(Aα). Further, the inclusion of A in C∗(G, A, α) induces an isomorphism from the purely positive part of the Cuntz semigroup Cu(A) to its image in Cu(C∗(G, A, α)). If α is strictly approximately inner, then in fact Cu(A) → Cu(C∗(G, A, α)) is an ordered semigroup isomorphism onto its range. Also, for every finite group G and for every η ∈ (0, 1/card(G)), we construct a simple separable unital AH algebra A with stable rank one and an approximately representable but pointwise outer action α: G → Aut(A) such that rc(A) = rc(C∗(G, A, α)) = η.
Permanent Link: https://hdl.handle.net/11104/0350812