Remarks on some simple $C^*$-algebras admitting a unique lower semicontinuous $2$-quasitrace

Jacopo Bassi

Remarks on some simple $C^*$-algebras admitting a unique lower semicontinuous $2$-quasitrace

Operator Algebras 2020-03-12 v2

Authors: Jacopo Bassi

Abstract

Using different descriptions of the Cuntz semigroup and of the Pedersen ideal, it is shown that $\sigma$ -unital simple $C^*$ -algebras with almost unperforated Cuntz semigroup, a unique lower semicontinuous $2$ -quasitrace and whose stabilization has almost stable rank $1$ are either stable or algebraically simple.

Keywords

simple C*-algebras Cuntz semigroup Pedersen ideal quasitrace stable rank algebraically simple

Cite

@article{arxiv.1806.08288,
  title  = {Remarks on some simple $C^*$-algebras admitting a unique lower semicontinuous $2$-quasitrace},
  author = {Jacopo Bassi},
  journal= {arXiv preprint arXiv:1806.08288},
  year   = {2020}
}

Comments

Replaced with accepted version, to appear in Colloquium Mathematicum

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