A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself

Details A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself

2010-01-21

arxiv.org/abs/1001.3890v1

Mathematics

Operator Algebras

24 pages; AMSLaTeX

Scientific paper

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. The construction can be generalized to any odd prime p such that -1 is not a square mod p, giving a C*-algebra D which has all the properties mentioned above, except D absorbs the p^{\infty} UHF algebra and one has p in place of 3 in the formula for the K-theory.

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