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Tikuisis, Aaron

The Cuntz semigroup of continuous functions into certain simple \(C^*\)-algebras. (English) Zbl 1232.46058

Int. J. Math. 22, No. 8, 1051-1087 (2011).
Summary: 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, \(\mathcal Z\)-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 \(C(\mathbb T, A)\). These results are a contribution towards the goal of using the Cuntz semigroup in the classification of well-behaved non-simple \(C^*\)-algebras.

Cited in 6 Documents

MSC:

46L35 Classifications of \(C^*\)-algebras
47L40 Limit algebras, subalgebras of \(C^*\)-algebras

Keywords:

Cuntz semigroup; approximately subhomogeneous \(C^*\)-algebras
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References:

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