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

  • Marius Dadarlat EMAIL logo und Ulrich Pennig
Veröffentlicht/Copyright: 13. März 2015

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 A𝕂 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.

Award Identifier / Grant number: #DMS–1101305

Funding statement: M. Dadarlat was partially supported by NSF grant #DMS–1101305.

Acknowledgements

The authors are grateful to Johannes Ebert, Peter May and Jim McClure for a number of useful discussions.

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Received: 2013-05-20
Revised: 2013-09-02
Published Online: 2015-03-13
Published in Print: 2016-09-01

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