The Brauer Semigroup of a groupoid and a symmetric imprimitivity theorem

Jonathan Henry Brown; Geoff Goehle

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arXiv · 1206.2064

The Brauer Semigroup of a groupoid and a symmetric imprimitivity theorem

Jonathan Henry Brown·Geoff Goehle

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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.

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Jonathan Henry Brown, Geoff Goehle. 2012-08-28. The Brauer Semigroup of a groupoid and a symmetric imprimitivity theorem. https://arxiv.org/abs/1206.2064

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