The radius of comparison of the crossed product by a weakly tracially strictly approximately inner action
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00582728" target="_blank" >RIV/67985840:_____/23:00582728 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4064/sm211002-5-4" target="_blank" >https://doi.org/10.4064/sm211002-5-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm211002-5-4" target="_blank" >10.4064/sm211002-5-4</a>
Alternative languages
Result language
angličtina
Original language name
The radius of comparison of the crossed product by a weakly tracially strictly approximately inner action
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Applications of C*-algebra classification: dynamics, geometry, and their quantum analogues</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studia mathematica
ISSN
0039-3223
e-ISSN
1730-6337
Volume of the periodical
271
Issue of the periodical within the volume
3
Country of publishing house
PL - POLAND
Number of pages
45
Pages from-to
241-285
UT code for WoS article
001124170500001
EID of the result in the Scopus database
2-s2.0-85171259623