Three applications of the cuntz semigroup

Nathanial P. Brown, Andrew S. Toms

Research output: Contribution to journalArticle

21 Scopus citations

Abstract

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
Volume2007
DOIs
StatePublished - Dec 1 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Three applications of the cuntz semigroup'. Together they form a unique fingerprint.

  • Cite this