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

Dadarlat Marius, Pennig Ulrich

Abstract

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