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

A. Tikuisis

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Abstract

This paper contains computations of the Cuntz semigroup of separable C*-algebras of the form C(X, A), where A is a unital, simple, Z-stable ASH algebra. The computations describe the Cuntz semigroup in terms of Murrayvon 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(double-struck T sign, A). These results are a contribution towards the goal of using the Cuntz semigroup in the classification of well-behaved non-simple C*-algebras.
Original languageEnglish
Pages (from-to)1051-1087
Number of pages37
JournalInternational Journal of Mathematics
Volume22
Issue number8
DOIs
Publication statusPublished - 1 Aug 2011

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Simple C*-algebras
Continuous Function
Semigroup
C*-algebra
Invariant
Unital
Algebra
Subset

Keywords

  • Cuntz semigroup
  • approximately subhomogeneous C*- algebras.

Cite this

The Cuntz semigroup of continuous functions into certain simple C*-algebras. / Tikuisis, A.

In: International Journal of Mathematics , Vol. 22, No. 8, 01.08.2011, p. 1051-1087.

Research output: Contribution to journalArticle

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