Weakly tracially approximately representable actions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00585183" target="_blank" >RIV/67985840:_____/24:00585183 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.7900/jot.2021dec07.2430" target="_blank" >https://doi.org/10.7900/jot.2021dec07.2430</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.7900/jot.2021dec07.2430" target="_blank" >10.7900/jot.2021dec07.2430</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Weakly tracially approximately representable actions

Popis výsledku v původním jazyce

We describe a weak tracial analog of approximate representability under the name “weak tracial approximate representability” for finite group actions. We then investigate the dual actions on the crossed products by this class of group actions. Namely, let G be a finite abelian group, let A be an infinite-dimensional simple unital C*-algebra, and let α: G → Aut(A) be an action of G on A which is pointwise outer. Then α has the weak tracial Rokhlin property if and only if the dual action αˆ of the Pontryagin dual Ĝ on the crossed product C*(G, A, α) is weakly tracially approximately representable, and α is weakly tracially approximately representable if and only if the dual action bα has the weak tracial Rokhlin property. This generalizes the results of Izumi in 2004 and Phillips in 2011 on the dual actions of finite abelian groups on unital simple C*-algebras.

Název v anglickém jazyce

Weakly tracially approximately representable actions

Popis výsledku anglicky

We describe a weak tracial analog of approximate representability under the name “weak tracial approximate representability” for finite group actions. We then investigate the dual actions on the crossed products by this class of group actions. Namely, let G be a finite abelian group, let A be an infinite-dimensional simple unital C*-algebra, and let α: G → Aut(A) be an action of G on A which is pointwise outer. Then α has the weak tracial Rokhlin property if and only if the dual action αˆ of the Pontryagin dual Ĝ on the crossed product C*(G, A, α) is weakly tracially approximately representable, and α is weakly tracially approximately representable if and only if the dual action bα has the weak tracial Rokhlin property. This generalizes the results of Izumi in 2004 and Phillips in 2011 on the dual actions of finite abelian groups on unital simple C*-algebras.

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

2024

Kód důvěrnosti údajů

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

Název periodika

Journal of Operator Theory

ISSN

0379-4024

e-ISSN

1841-7744

Svazek periodika

91

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

RO - Rumunsko

Počet stran výsledku

23

Strana od-do

3-25

Kód UT WoS článku

001185553600004

EID výsledku v databázi Scopus

2-s2.0-85189334273