A simple, monotracial, stably projectionless C*-algebra

作者：Jacelon Bhishan^*

来源：Journal of the London Mathematical Society-Second Series, 2013, 87(2): 365-383.

DOI：10.1112/jlms/jds049

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 non-degenerate endomorphism of W is approximately inner and we construct a trace-preserving embedding of W into the central sequences algebra M(W)(infinity)boolean AND W%26apos;. We conjecture that W circle times W congruent 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.

• 出版日期2013-4