The weak tracial Rokhlin property for finite group actions on simple C*-algebras
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
The weak tracial Rokhlin property for finite group actions on simple C*-algebras
Original language description
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.
Czech name
—
Czech description
—
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Documenta Mathematica
ISSN
1431-0643
e-ISSN
—
Volume of the periodical
25
Issue of the periodical within the volume
October
Country of publishing house
DE - GERMANY
Number of pages
46
Pages from-to
2507-2552
UT code for WoS article
000617388400017
EID of the result in the Scopus database
2-s2.0-85102342181