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arXiv · 1006.5397

A simple, monotracial, stably projectionless C*-algebra

Bhishan Jacelon
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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.

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Bhishan Jacelon. 2010-06-28. A simple, monotracial, stably projectionless C*-algebra. https://arxiv.org/abs/1006.5397

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