Three applications of the cuntz semigroup

Nathanial P. Brown, Andrew S. Toms

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26 Scopus citations


Building on work of Elliott and coworkers, we present three applications of the Cuntz semigroup: (i) 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; (ii) for the algebras in (i), classification of their Hilbert modules is similar to the von Neumann algebra context; (iii) for the algebras in (i), approximate unitary equivalence of self-adjoint operators is characterised in terms of the Elliott invariant.

Original languageEnglish (US)
Article numberrnm068
JournalInternational Mathematics Research Notices
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • General Mathematics


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