C*-algebras associated to homeomorphisms twisted by vector bundles over finite dimensional spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00582707" target="_blank" >RIV/67985840:_____/24:00582707 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/24:00372448
Result on the web
<a href="https://doi.org/10.1090/tran/8900" target="_blank" >https://doi.org/10.1090/tran/8900</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/tran/8900" target="_blank" >10.1090/tran/8900</a>
Alternative languages
Result language
angličtina
Original language name
C*-algebras associated to homeomorphisms twisted by vector bundles over finite dimensional spaces
Original language description
In this paper we study Cuntz-Pimsner algebras associated to C*-correspondences over commutative C*-algebras from the point of view of the C*-algebra classification programme. We show that when the correspondence comes from an aperiodic homeomorphism of a finite dimensional infinite compact metric space X twisted by a vector bundle, the resulting Cuntz- Pimsner algebras have finite nuclear dimension. When the homeomorphism is minimal, this entails classification of these C*-algebras by the Elliott invariant. This establishes a dichotomy: when the vector bundle has rank one, the Cuntz-Pimsner algebra has stable rank one. Otherwise, it is purely infinite. For a Cuntz-Pimsner algebra of a minimal homeomorphism of an infinite compact metric space X twisted by a line bundle over X, we introduce orbit breaking subalgebras. With no assumptions on the dimension of X, we show that they are centrally large subalgebras and hence simple and stably finite. When the dimension of X is finite, they are furthermore Z-stable and hence classified by the Elliott invariant.
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
Result was created during the realization of more than one project. More information in the Projects tab.
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
American Mathematical Society. Transactions
ISSN
0002-9947
e-ISSN
1088-6850
Volume of the periodical
377
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
44
Pages from-to
1597-1640
UT code for WoS article
001150330300001
EID of the result in the Scopus database
2-s2.0-85185603548