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

Jacopo Bassi

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arXiv · 1806.08288

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

Jacopo Bassi

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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.

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Jacopo Bassi. 2018-06-21. Remarks on some simple $C^*$-algebras admitting a unique lower semicontinuous $2$-quasitrace. https://arxiv.org/abs/1806.08288

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