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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Aplikace klasifikace C*-algeber: dynamika, geometrie a jejich kvantové analogie</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Studia mathematica

ISSN

0039-3223

e-ISSN

1730-6337

Svazek periodika

271

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

45

Strana od-do

241-285

Kód UT WoS článku

001124170500001

EID výsledku v databázi Scopus

2-s2.0-85171259623