The Brauer Semigroup of a groupoid and a symmetric imprimitivity theorem

2012/06/10 by Jonathan H. Brown, Jonathan Henry Brown, Brown, Jonathan Henry +2 · 1 citation
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1206.2064

30 pages, minor changes in the wording of the introduction

openalex publication_date 2012/06/10 · arxiv created 2012/08/28 · arxiv updated 2012/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we define a monoid called the equivariant Brauer semigroup for a locally compact Hausdorff groupoid E whose elements consist of Morita equivalence classes of E-dynamical systems. This construction generalizes both the equivariant Brauer semigroup for transformation groups and the equivariant Brauer group for a groupoid. We show that groupoid equivalence induces an isomorphism of equivariant Brauer semigroups and that this isomorphism preserves the Morita equivalence classes of the respective crossedproducts, thus generalizing Raeburn's symmetric imprimitivity theorem.

Cited by

• Groupoid equivalence and the associated iterated crossed product

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