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arXiv · 1110.1390

Regularity for stably projectionless, simple C*-algebras

Aaron Tikuisis
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Abstract

This paper explores the following regularity properties and their relationships for simple, not-necessarily-unital C*-algebras: (i) Jiang-Su stability, (ii) Unperforation in the Cuntz semigroup, and (iii) slow dimension growth (applying only in the case that the C*-algebra is approximately subhomogeneous). An example is given of a simple, separable, nuclear, stably projectionless C*-algebra whose Cuntz semigroup is not almost unperforated. This example is in fact approximately subhomogeneous. It is also shown that, in contrast to this example, when an approximately subhomogeneous simple C*-algebra has slow dimension growth, its Cuntz semigroup is necessarily almost unperforated.

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Aaron Tikuisis. 2012-07-17. Regularity for stably projectionless, simple C*-algebras. https://doi.org/10.1016/j.jfa.2012.05.020

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