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

Dadarlat, Marius and Pennig, Ulrich ORCID: https://orcid.org/0000-0001-5441-6130 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:	14 Nov 2024 17:00
URI:	https://orca.cardiff.ac.uk/id/eprint/89485

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