A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself
Operator Algebras
2014-01-22 v2
Abstract
We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3^{\infty} UHF algebra. We can also explicitly compute the K-theory of D, namely K_0 (D) = Z[1/3] with the standard order, and K_1 (D) = 0, as well as the Cuntz semigroup of D.
Keywords
Cite
@article{arxiv.1001.3890,
title = {A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself},
author = {N. Christopher Phillips and Maria Grazia Viola},
journal= {arXiv preprint arXiv:1001.3890},
year = {2014}
}
Comments
16 pages; AMSLaTeX. The material on other possible K-groups for such an algebra has been moved to a separate paper (1309.4142 [math.OA])