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 language | English (US) |
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Article number | rnm068 |
Journal | International Mathematics Research Notices |
Volume | 2007 |
DOIs | |
State | Published - 2007 |
All Science Journal Classification (ASJC) codes
- General Mathematics