The descriptive set theory of C∗-algebra invariants

Ilijas Farah; Andrew Toms; Asger Dag Törnquist

doi:10.1093/imrn/rns206

The descriptive set theory of C∗-algebra invariants

Ilijas Farah, Andrew Toms, Asger Dag Törnquist

Institut for Matematiske Fag

14 Citationer (Scopus)

Abstract

We establish the Borel computability of various C*-algebra invariants, including the Elliott invariant and the Cuntz semigroup. As applications, we deduce that AF algebras are classifiable by countable structures, and that a conjecture of Winter and the second author for nuclear separable simple C*-algebras cannot be disproved by appealing to known standard Borel structures on these algebras.

Originalsprog	Engelsk
Tidsskrift	International Mathematics Research Notices
Vol/bind	2013
Udgave nummer	22
Sider (fra-til)	5196–5226
ISSN	1073-7928
DOI	https://doi.org/10.1093/imrn/rns206
Status	Udgivet - 1 jan. 2013

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10.1093/imrn/rns206

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AB - We establish the Borel computability of various C*-algebra invariants, including the Elliott invariant and the Cuntz semigroup. As applications, we deduce that AF algebras are classifiable by countable structures, and that a conjecture of Winter and the second author for nuclear separable simple C*-algebras cannot be disproved by appealing to known standard Borel structures on these algebras.

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The descriptive set theory of C∗-algebra invariants

Abstract

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