The Brauer semigroup of a groupoid and a symmetric imprimitivity theorem

Brown, Jonathan; Goehle, Geoff

doi:10.1090/S0002-9947-2013-05953-3

The Brauer semigroup of a groupoid and a symmetric imprimitivity theorem
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by Jonathan Henry Brown and Geoff Goehle PDF

Trans. Amer. Math. Soc. 366 (2014), 1943-1972 Request permission

Abstract:

In this paper we define a monoid called the 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 Brauer group for a groupoid. We show that groupoid equivalence induces an isomorphism of Brauer semigroups and that this isomorphism preserves the Morita equivalence classes of the respective crossed products, thus generalizing Raeburn’s symmetric imprimitivity theorem.

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