Journal of Operator Theory

Volume 36, Issue 1, Summer 1996 pp. 73-105.

The equivariant Brauer groups of principal bundles

Authors: Judith A. Packer (1), Iain Raeburn (2) and Dana P. Williams (3)
Author institution:(1) Department of Mathematics, National University of Singapore, Kent Ridge 0511, SINGAPORE
(2) Department of Mathematics, University of Newcastle, Newcastle, NSW 2308, AUSTRALIA
(3) Department of Mathematics, Dartmouth College, Hanover, NH 03755-3551, USA

Summary: We study the structure of the equivariant Brauer group Br_G(T) of a principal G/N-bundle by exhibiting a filtration of Br_G(T) predicted by a spectral sequence of Grothendieck’s in the case of finite G. The first ingredient $M(A, \alpha)$ is the Mackey obstruction to implementing $\alpha | N$ by a unitary group. The kernel of M can be identified with an equivariant cohomology group $H_G^2 (T, \mathcal S)$, and our main theorem makes four nontrivial assertions about this group. Our constructions extend to higher dimensional groups $H_G^n (T, \mathcal S)$, and we show that there is a long exact sequence involving these groups generalizing the usual Gysin sequence associated to a principal circle bundle.

Keywords: Brauer group, continuous trace, Dixmier-Douady class.

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