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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Brauer semigroup of a groupoid and a symmetric imprimitivity theorem


Authors: Jonathan Henry Brown and Geoff Goehle
Journal: Trans. Amer. Math. Soc. 366 (2014), 1943-1972
MSC (2010): Primary 46L55, 22A22
Published electronically: October 31, 2013
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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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Additional Information

Jonathan Henry Brown
Affiliation: Department of Mathematics, 138 Cardwell Hall, Kansas State University, Manhattan, Kansas 66506-2602
Email: brownjh@math.kansas.edu

Geoff Goehle
Affiliation: Mathematics and Computer Science Department, Stillwell 426, Western Carolina University, Cullowhee, North Carolina 28723
Email: grgoehle@email.wcu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05953-3
PII: S 0002-9947(2013)05953-3
Keywords: Groupoids, crossed products, equivalence theorem, symmetric imprimitivity theorem
Received by editor(s): June 12, 2012
Published electronically: October 31, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.