The weak tracial Rokhlin property for finite group actions on simple C*-algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00540209" target="_blank" >RIV/67985840:_____/20:00540209 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.25537/dm.2020v25.2507-2552" target="_blank" >http://dx.doi.org/10.25537/dm.2020v25.2507-2552</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.25537/dm.2020v25.2507-2552" target="_blank" >10.25537/dm.2020v25.2507-2552</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The weak tracial Rokhlin property for finite group actions on simple C*-algebras

Popis výsledku v původním jazyce

We develop the concept of weak tracial Rokhlin property for finite group actions on simple (not necessarily unital) C*-algebras and study its properties systematically. In particular, we show that this property is stable under restriction to invariant hereditary C*-algebras, minimal tensor products, and direct limits of actions. Some of these results are new even in the unital case and answer open questions asked by N. C. Phillips in full generality. We present several examples of finite group actions with the weak tracial Rokhlin property on simple stably projectionless C*-algebras. We prove that if α:G→Aut(A) is an action of a finite group G on a simple C*-algebra A with tracial rank zero and α has the weak tracial Rokhlin property, then the crossed product A⋊αG and the fixed point algebra Aα are simple with tracial rank zero. This extends a result of N. C. Phillips to the nonunital case. We use the machinery of Cuntz subequivalence to work in this nonunital setting.

Název v anglickém jazyce

The weak tracial Rokhlin property for finite group actions on simple C*-algebras

Popis výsledku anglicky

We develop the concept of weak tracial Rokhlin property for finite group actions on simple (not necessarily unital) C*-algebras and study its properties systematically. In particular, we show that this property is stable under restriction to invariant hereditary C*-algebras, minimal tensor products, and direct limits of actions. Some of these results are new even in the unital case and answer open questions asked by N. C. Phillips in full generality. We present several examples of finite group actions with the weak tracial Rokhlin property on simple stably projectionless C*-algebras. We prove that if α:G→Aut(A) is an action of a finite group G on a simple C*-algebra A with tracial rank zero and α has the weak tracial Rokhlin property, then the crossed product A⋊αG and the fixed point algebra Aα are simple with tracial rank zero. This extends a result of N. C. Phillips to the nonunital case. We use the machinery of Cuntz subequivalence to work in this nonunital setting.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Documenta Mathematica

ISSN

1431-0643

e-ISSN

—

Svazek periodika

25

Číslo periodika v rámci svazku

October

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

46

Strana od-do

2507-2552

Kód UT WoS článku

000617388400017

EID výsledku v databázi Scopus

2-s2.0-85102342181