A generalization of the topological Brauer group

Abstract

In the present paper we study some homotopy invariants which can be defined by means of bundles with fiber a matrix algebra. We also introduce some generalization of the Brauer group in the topological context and show that any its element can be represented as a locally trivial bundle with a group of invertible operators in a Hilbert space as the structure group. Finally, we discuss its possible applications in the twisted $K$-theory.

34 pages. v5: The part concerning the generalized Brauer group has been completely rewritten. An application to twisted $K$-theory is added

References in corpus (5)

• The index of projective families of elliptic operators
• The topology of T-duality for T^n-bundles
• A Dixmier-Douady theory for strongly self-absorbing C*-algebras
• A Dixmier-Douady Theory for strongly self-absorbing C*-algebras II: the Brauer group
• Topological obstructions to embedding of a matrix algebra bundle into a trivial one