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The Cuntz semigroup of unital commutative AI-algebras

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  18 October 2022

Eduard Vilalta Open the ORCID record for Eduard Vilalta [Opens in a new window]
Eduard Vilalta*
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Spain
*
e-mail: evilalta@mat.uab.cat
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Abstract

We provide an abstract characterization for the Cuntz semigroup of unital commutative AI-algebras, as well as a characterization for abstract Cuntz semigroups of the form $\operatorname {\mathrm {Lsc}} (X,\overline {\mathbb {N}})$ for some $T_1$-space X. In our investigations, we also uncover new properties that the Cuntz semigroup of all AI-algebras satisfies.

Keywords

C*-algebrasCuntz semigroupsAI-algebras

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L85: Noncommutative topology
Type
Article
Information
Canadian Journal of Mathematics , Volume 75 , Issue 6 , December 2023 , pp. 1831 - 1868
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

The author was partially supported by the MINECO (Grant Nos. PRE2018-083419 and MTM2017-83487-P) and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya (Grant No. 2017SGR01725).

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