Three Applications of the Cuntz Semigroup

@misc{citeulike:1923513, 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.}, author = {Brown, Nathanial P. and Toms, Andrew S. }, citeulike-article-id = {1923513}, eprint = {0704.3988}, keywords = {classification}, month = {Apr}, posted-at = {2007-11-15 18:14:44}, priority = {2}, title = {Three Applications of the Cuntz Semigroup}, url = {http://arxiv.org/abs/0704.3988}, year = {2007} }

TY - ELEC ID - citeulike:1923513 L3 - citeulike-article-id:1923513 N2 - 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. TI - Three Applications of the Cuntz Semigroup KW - classification AU - Brown, Nathanial AU - Toms, Andrew PY - 2007/Apr/30/ UR - http://arxiv.org/abs/0704.3988 ER -