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: | 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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