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

Dadarlat, Marius and Pennig, Ulrich ORCID: https://orcid.org/0000-0001-5441-6130 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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Abstract

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:	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:	06 Dec 2024 15:00
URI:	https://orca.cardiff.ac.uk/id/eprint/89458

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