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A Dixmier-Douady theory for strongly self-absorbing C*-algebras II: the Brauer group

Dadarlat, Marius and Pennig, Ulrich 2016. A Dixmier-Douady theory for strongly self-absorbing C*-algebras II: the Brauer group. Journal of Noncommutative Geometry 9 (4) , pp. 1137-1154. 10.4171/JNCG/218

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Abstract

We have previously shown that the isomorphism classes of orientable locally trivial fields of C∗-algebras over a compact metrizable space X with fiber D⊗K, where D is a strongly self-absorbing C∗-algebra, form an abelian group under the operation of tensor product. Moreover this group is isomorphic to the first group E¯1D(X) of the (reduced) generalized cohomology theory associated to the unit spectrum of topological K-theory with coefficients in D. Here we show that all the torsion elements of the group E¯1D(X) arise from locally trivial fields with fiber D⊗Mn(C), n≥1, for all known examples of strongly self-absorbing C∗-algebras} D. Moreover the Brauer group generated by locally trivial fields with fiber D⊗Mn(C), n≥1 is isomorphic to TorE¯1D(X).

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: European Mathematical Society
ISSN: 1661-6952
Date of First Compliant Deposit: 2 December 2016
Last Modified: 13 Mar 2020 00:57
URI: http://orca.cf.ac.uk/id/eprint/89485

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  • A Dixmier-Douady theory for strongly self-absorbing C*-algebras II: the Brauer group. (deposited 21 Apr 2016 10:21) [Currently Displayed]

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