Turbulence, orbit equivalence, and the classification of nuclear C∗-algebras
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
We bound the Borel cardinality of the isomorphism relation for nuclear simple separable C*-algebras: It is turbulent, yet Borel reducible to the action of the automorphism group of the Cuntz algebra O2
on its closed subsets. The same bounds are obtained for affine
homeomorphism of metrizable Choquet simplexes. As a by-product we
recover a result of Kechris and Solecki, namely, that homeomorphism of
compacta in the Hilbert cube is Borel reducible to a Polish group
action. These results depend intimately on the classification theory of
nuclear simple C*-algebras by K-theory and traces. Both of necessity and in order to lay the groundwork for further study on the Borel complexity of C*-algebras, we prove that many standard C*-algebra constructions and relations are Borel, and we prove Borel versions of Kirchberg's O2-stability and embedding theorems. We also find a C*-algebraic witness for a Kσ hard equivalence relation.
Originalsprog | Engelsk |
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Tidsskrift | Journal fuer die Reine und Angewandte Mathematik |
Udgave nummer | 688 |
Sider (fra-til) | 101-146 |
ISSN | 0075-4102 |
DOI | |
Status | Udgivet - 2014 |
ID: 135505703