Three Applications of the Cuntz Semigroup

Building on work of Elliott and coworkers, we present three applications of the Cuntz semigroup: for many simple C*-algebras, the Thomsen semigroup is recovered functorially from the Elliott invariant, and this yields a new proof of Elliott's classification theorem for simple, unital AI algebra...

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Bibliographic Details
Published in:International mathematics research notices 2007, Vol.2007
Main Authors: Brown, Nathanial P., Toms, Andrew S.
Format: Article
Language:English
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Summary:Building on work of Elliott and coworkers, we present three applications of the Cuntz semigroup: for many simple C*-algebras, the Thomsen semigroup is recovered functorially from the Elliott invariant, and this yields a new proof of Elliott's classification theorem for simple, unital AI algebras; for the algebras in (i), classification of their Hilbert modules is similar to the von Neumann algebra context; for the algebras in (i), approximate unitary equivalence of self-adjoint operators is characterised in terms of the Elliott invariant.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnm068