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

Abstract

We show that the Dixmier-Douady theory of continuous field $C^{\ast }$-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.

26p, this version agrees with the one published in J. Reine Angew. Math. except for a minor correction and an extension of Corollary 4.8, both of which were done after publication

References in corpus (5)

• Strongly self-absorbing C*-algebras are Z-stable
• C_0(X)-algebras, stability and strongly self-absorbing C*-algebras
• Trivialization of C(X)-algebras with strongly self-absorbing fibres
• Fiberwise KK-equivalence of continuous fields of C*-algebras
• Fundamental group of simple $C^{\ast }$-algebras with unique trace

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• Bundles of strongly self-absorbing $C^{\ast }$-algebras with a Clifford grading