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The Cuntz semigroup of unital commutative AI-algebras

Published online by Cambridge University Press:  18 October 2022

Eduard Vilalta*
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Spain

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.

Type
Article
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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