Towards a classification of unitary elements of C*-algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00618864" target="_blank" >RIV/67985840:_____/25:00618864 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1093/imrn/rnaf068" target="_blank" >https://doi.org/10.1093/imrn/rnaf068</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imrn/rnaf068" target="_blank" >10.1093/imrn/rnaf068</a>

Result language
angličtina
Original language name
Towards a classification of unitary elements of C*-algebras
Original language description
In [5] the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We provide a complete proof by addressing the existence part of the conjecture, under a mild adjustment of both domain and codomain of the functor Cu. We also tackle the classification beyond the AF case and more particularly, we look at unitary elements of what we call AH1-algebras. We obtain positive progress as far as the existence part is concerned. Nevertheless, we reveal that extra information is needed for the uniqueness part of the classification that the Cuntz semigroup fails to capture.
Czech name
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Czech description
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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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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