Turbulence, orbit equivalence, and the classification of nuclear C∗-algebras

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Standard

Turbulence, orbit equivalence, and the classification of nuclear C∗-algebras. / Farah, Ilijas; Toms, Andrew; Törnquist, Asger Dag.

I: Journal fuer die Reine und Angewandte Mathematik, Nr. 688, 2014, s. 101-146.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Farah, I, Toms, A & Törnquist, AD 2014, 'Turbulence, orbit equivalence, and the classification of nuclear C∗-algebras', Journal fuer die Reine und Angewandte Mathematik, nr. 688, s. 101-146. https://doi.org/10.1515/crelle-2012-0053

APA

Farah, I., Toms, A., & Törnquist, A. D. (2014). Turbulence, orbit equivalence, and the classification of nuclear C∗-algebras. Journal fuer die Reine und Angewandte Mathematik, (688), 101-146. https://doi.org/10.1515/crelle-2012-0053

Vancouver

Farah I, Toms A, Törnquist AD. Turbulence, orbit equivalence, and the classification of nuclear C∗-algebras. Journal fuer die Reine und Angewandte Mathematik. 2014;(688):101-146. https://doi.org/10.1515/crelle-2012-0053

Author

Farah, Ilijas ; Toms, Andrew ; Törnquist, Asger Dag. / Turbulence, orbit equivalence, and the classification of nuclear C∗-algebras. I: Journal fuer die Reine und Angewandte Mathematik. 2014 ; Nr. 688. s. 101-146.

Bibtex

@article{8db7019757c149f8ba7583bd24e0d9c6,
title = "Turbulence, orbit equivalence, and the classification of nuclear C∗-algebras",
abstract = "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. ",
author = "Ilijas Farah and Andrew Toms and T{\"o}rnquist, {Asger Dag}",
year = "2014",
doi = "10.1515/crelle-2012-0053",
language = "English",
pages = "101--146",
journal = "Journal fuer die Reine und Angewandte Mathematik",
issn = "0075-4102",
publisher = "Walterde Gruyter GmbH",
number = "688",

}

RIS

TY - JOUR

T1 - Turbulence, orbit equivalence, and the classification of nuclear C∗-algebras

AU - Farah, Ilijas

AU - Toms, Andrew

AU - Törnquist, Asger Dag

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

U2 - 10.1515/crelle-2012-0053

DO - 10.1515/crelle-2012-0053

M3 - Journal article

SP - 101

EP - 146

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

SN - 0075-4102

IS - 688

ER -

ID: 135505703