Regularity for stably projectionless, simple C*-algebras

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.

26 pages. Minor edits have been made

References in corpus (5)

• The stable and the real rank of Z-absorbing C*-algebras
• A Note On Subhomogeneous C*-Algebras
• Nuclear dimension and n-comparison
• Comparison theory and smooth minimal C*-dynamics
• Hilbert C*-modules over a commutative C*-algebra

Cited by in corpus (6)

• Nuclear dimension, Z-stability, and algebraic simplicity for stably projectionless C*-algebras
• Picard groups of certain stably projectionless C*-algebras
• Equivariant property (SI) revisited
• On the structure of the Cuntz semigroup in (possibly) nonunital C*-algebras
• Remarks on Z-stable projectionless C*-algebras
• Corrigendum to "Regularity for stably projectionless, simple C*-algebras"