The Cuntz semigroup of unital commutative AI-algebras

Eduard Vilalta

The Cuntz semigroup of unital commutative AI-algebras

Operator Algebras 2021-04-19 v1

Authors: Eduard Vilalta

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 $\text{Lsc} (X,\overline{\mathbb{N}})$ for some $T_1$ -space $X$ . In our investigations, we also uncover new properties that the Cuntz semigroup of all AI-algebras satisfies.

Keywords

cuntz semigroup ai-algebras commutative algebras t1-space lower semicontinuous functions

Cite

@article{arxiv.2104.08165,
  title  = {The Cuntz semigroup of unital commutative AI-algebras},
  author = {Eduard Vilalta},
  journal= {arXiv preprint arXiv:2104.08165},
  year   = {2021}
}

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33 pages

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