Weakly tracially approximately representable actions
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Weakly tracially approximately representable actions
Original language description
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.
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
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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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Operator Theory
ISSN
0379-4024
e-ISSN
1841-7744
Volume of the periodical
91
Issue of the periodical within the volume
1
Country of publishing house
RO - ROMANIA
Number of pages
23
Pages from-to
3-25
UT code for WoS article
001185553600004
EID of the result in the Scopus database
2-s2.0-85189334273