The descriptive set theory of C^*-algebra invariants

2011/12/15 by Ilijas Farah, Farah, Ilijas, Andrew S. Toms +3
Mathematics · #FOS: Mathematics #Logic (math.LO) #Operator Algebras (math.OA) #math.LO #math.OA

paper · pdf · doi:10.48550/arxiv.1112.3576

Appendix with Caleb Eckhardt

arxiv created 2012/04/21 · arxiv updated 2015/03/12

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.

Related

• A systematic approach for invariants of C*-algebras
• The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras
• K-Theory for operator algebras. Classification of C^*-algebras
• About the Cuntz Comparison for Non-simple C*-algebras
• Three Applications of the Cuntz Semigroup