A simple, monotracial, stably projectionless C*-algebra

Abstract

We construct a simple, nuclear, stably projectionless C*-algebra W which has trivial K-theory and a unique tracial state, and we investigate the extent to which W might fit into the hierarchy of strongly self-absorbing C*-algebras as an analogue of the Cuntz algebra O_2. In this context, we show that every nondegenerate endomorphism of W is approximately inner and we construct a trace-preserving embedding of W into the central sequences algebra M(W)_\infty \cap W'. We conjecture that W\otimes W is isomorphic to W and we note some implications of this, for example that W would be absorbed tensorially by a certain class of nuclear, stably projectionless C*-algebras. Finally, we explain why W may play some role in the classification of such algebras.

16 pages; Theorem 5.1 is now Conjecture 5.1; to appear in J. London Math. Soc

References in corpus (2)

• Completely positive maps of order zero
• Strongly self-absorbing C*-algebras are Z-stable

Cited by in corpus (2)

• Picard groups of certain stably projectionless C*-algebras
• Fundamental group of simple $C^{\ast }$-algebras with unique trace