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Decomposition rank of approximately subhomogeneous C*-algebras

Decomposition rank of approximately subhomogeneous C*-algebras AbstractIt is shown that every Jiang–Su stable approximately subhomogeneous C*{{\mathrm{C}^{*}}}-algebra has finite decomposition rank.This settles a key direction of the Toms–Winter conjecture for simple approximately subhomogeneous C*{{\mathrm{C}^{*}}}-algebras.A key step in the proof is that subhomogeneous C*{{\mathrm{C}^{*}}}-algebras are locally approximated by a certain class of more tractable subhomogeneous algebras, namely a non-commutative generalization of the class of cell complexes.The result is applied, in combination with other recent results, to show classifiability of crossed product C*{{\mathrm{C}^{*}}}-algebras associated to minimal homeomorphisms with mean dimension zero. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Decomposition rank of approximately subhomogeneous C*-algebras

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Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2020-0018
Publisher site
See Article on Publisher Site

Abstract

AbstractIt is shown that every Jiang–Su stable approximately subhomogeneous C*{{\mathrm{C}^{*}}}-algebra has finite decomposition rank.This settles a key direction of the Toms–Winter conjecture for simple approximately subhomogeneous C*{{\mathrm{C}^{*}}}-algebras.A key step in the proof is that subhomogeneous C*{{\mathrm{C}^{*}}}-algebras are locally approximated by a certain class of more tractable subhomogeneous algebras, namely a non-commutative generalization of the class of cell complexes.The result is applied, in combination with other recent results, to show classifiability of crossed product C*{{\mathrm{C}^{*}}}-algebras associated to minimal homeomorphisms with mean dimension zero.

Journal

Forum Mathematicumde Gruyter

Published: Jul 1, 2020

References