Three applications of the cuntz semigroup

Nathanial P. Brown, Andrew S. Toms

Research output: Contribution to journalArticle

21 Citations (Scopus)

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

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Semigroup
Algebra
Hilbert Modules
Simple C*-algebras
Invariant
Von Neumann Algebra
Unital
Self-adjoint Operator
Equivalence
Theorem
Context

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Three applications of the cuntz semigroup. / Brown, Nathanial P.; Toms, Andrew S.

In: International Mathematics Research Notices, Vol. 2007, rnm068, 01.12.2007.

Research output: Contribution to journalArticle

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