The Cuntz semigroup of continuous functions into certain simple C*-algebras

Details The Cuntz semigroup of continuous functions into certain simple C*-algebras The Cuntz semigroup of continuous functions into certain simple C*-algebras

2010-07-17

arxiv.org/abs/1007.2927v3

Mathematics

Operator Algebras

37 pages. To appear in International Journal of Mathematics

Scientific paper

This paper contains computations of the Cuntz semigroup of separable C*-algebras of the form C_0(X,A), where A is a unital, simple, Z-stable ASH algebra. The computations describe the Cuntz semigroup in terms of Murray-von Neumann semigroups of C(K,A) for compact subsets K of X. In particular, the computation shows that the Elliott invariant is functorially equivalent to the invariant given by the Cuntz semigroup of C(T,A). These results are a contribution towards the goal of using the Cuntz semigroup in the classification of well-behaved non-simple C*-algebras.

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