A generalization of the topological Brauer group

2003/01/16 by A. V. Ershov, Ershov, A. V.
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AT #math.KT

paper · pdf · doi:10.48550/arxiv.math/0301180

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

arxiv created 2005/11/18 · arxiv updated 2009/11/30

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.

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