A systematic approach for invariants of C∗-algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00582791" target="_blank" >RIV/67985840:_____/23:00582791 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4064/sm230516-22-6" target="_blank" >https://doi.org/10.4064/sm230516-22-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm230516-22-6" target="_blank" >10.4064/sm230516-22-6</a>

Result language
angličtina
Original language name
A systematic approach for invariants of C∗-algebras
Original language description
We define a categorical framework in which we build a systematic construction that provides generic invariants for C∗-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties such as continuity, a metric on the set of morphisms and a theory of ideals and quotients which naturally encapsulates compatibility diagrams. Consequently, any of these invariants appear as good candidates for the classification of non-simple C∗-algebras. Further, most of the existing invariants could be rewritten via this method. As an application, we define a Hausdorffized version of the unitary Cuntz semigroup and explore its potential towards classification results. We indicate several open lines of research.
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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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