The K-Theory of a Simple Separable Exact C*-Algebra Not Isomorphic to Its Opposite Algebra

2013/09/17 by Phillips, N. Christopher, Viola, Maria Grazia
#46L35 (Primary) 46L37 #46L40 #46L54 (Secondary) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1309.4142

Abstract

We construct uncountably many mutually nonisomorphic simple separable stably finite unital exact C^∗-algebras which are not isomorphic to their opposite algebras. In particular, we prove that there are uncountably many possibilities for the K₀-group, the K₁-group, and the tracial state space of such an algebra. We show that these C*-algebras satisfy the Universal Coefficient Theorem. This is new even for the already known example of an exact C*-algebra nonisomorphic to its opposite algebra produced in earlier work.

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