Keyword: Cuntz Semigroup : Search

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articleNo Access
COMPLETIONS OF MONOIDS WITH APPLICATIONS TO THE CUNTZ SEMIGROUP
- RAMON ANTOINE,
- JOAN BOSA, and
- FRANCESC PERERA
International Journal of Mathematics01 Jun 2011
Preview Abstract
We provide an abstract categorical framework that relates the Cuntz semigroups of the C*-algebras A and . This is done through a certain completion of ordered monoids by adding suprema of countable ascending sequences. Our construction is rather explicit and we show it is functorial and unique up to isomorphism. This approach is used in some applications to compute the stabilized Cuntz semigroup of certain C*-algebras.
articleNo Access
THE CUNTZ SEMIGROUP OF CONTINUOUS FUNCTIONS INTO CERTAIN SIMPLE C*-ALGEBRAS
- AARON TIKUISIS
International Journal of Mathematics01 Aug 2011
Preview Abstract
This paper contains computations of the Cuntz semigroup of separable C*-algebras of the form C₀(X, A), where A is a unital, simple, -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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