A simple, self-absorbing, stably projectionless C*-algebra

Details A simple, self-absorbing, stably projectionless C*-algebra A simple, self-absorbing, stably projectionless C*-algebra

2010-06-28

arxiv.org/abs/1006.5397v2

Mathematics

Operator Algebras

16 pages; incorrect proof of Theorem 5.1 removed; new result on W-stability added; minor corrections made

Scientific paper

We construct a simple, nuclear, stably projectionless C*-algebra W which has trivial K-theory and a unique tracial state, and we prove that W shares some of the important properties of the Cuntz algebra O_2. In particular, 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 observe that W\otimes W is isomorphic to W (a fact which will be proved in a forthcoming article by Leonel Robert) and we deduce from this that W is absorbed tensorially by a 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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