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arXiv · 1302.4468

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

Marius Dadarlat·Ulrich Pennig
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Abstract

We show that the Dixmier-Douady theory of continuous field $C^*$-algebras with compact operators $\mathbb{K}$ as fibers extends significantly to a more general theory of fields with fibers $A\otimes \mathbb{K}$ 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.

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Marius Dadarlat, Ulrich Pennig. 2013-02-18. A Dixmier-Douady theory for strongly self-absorbing C*-algebras. https://doi.org/10.1515/crelle-2014-0044

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