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A Dixmier--Douady theory for strongly self-absorbing C*-algebras

Dadarlat, Marius and Pennig, Ulrich 2016. A Dixmier--Douady theory for strongly self-absorbing C*-algebras. Journal für die reine und angewandte Mathematik 2016 (718) , pp. 153-181. 10.1515/crelle-2014-0044

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We show that the Dixmier–Douady theory of continuous fields of C*-algebras with compact operators K as fibers extends significantly to a more general theory of fields with fibers A ⊗ K where A is a strongly self-absorbing C∗-algebra. The classification of the corresponding locally trivial fields involves a generalized cohomology theory which is computable via the Atiyah–Hirzebruch spectral sequence. An important feature of the general theory is the appearance of characteristic classes in higher dimensions. We also give a necessary and sufficient K-theoretical condition for local triviality of these continuous fields over spaces of finite covering dimension.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: De Gruyter
ISSN: 1435-5345
Date of First Compliant Deposit: 2 December 2016
Date of Acceptance: 2 September 2013
Last Modified: 19 Nov 2020 10:30

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