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COMPLETIONS OF MONOIDS WITH APPLICATIONS TO THE CUNTZ SEMIGROUP

RAMON ANTOINE

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

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JOAN BOSA

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

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, and

FRANCESC PERERA

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

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https://doi.org/10.1142/S0129167X11007057Cited by:17 (Source: Crossref)

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.

Keywords:

AMSC: 06F05, 46L35, 19K14

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