A Dixmier-Douady Theory for strongly self-absorbing C*-algebras II: the Brauer group

Dadarlat Marius, Pennig Ulrich

Zusammenfassung

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^1_D(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^1_D(X) arise from locally trivial fields with fiber D⊗M_n(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⊗M_n(ℂ), n≥1 is isomorphic to Tor(E^1_D(X)).