Remote Access Transactions of the American Mathematical Society
Green Open Access

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
MathSciNet review: 3152718
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 46L55, 22A22

Retrieve articles in all journals with MSC (2010): 46L55, 22A22

Additional Information

Jonathan Henry Brown
Affiliation: Department of Mathematics, 138 Cardwell Hall, Kansas State University, Manhattan, Kansas 66506-2602

Geoff Goehle
Affiliation: Mathematics and Computer Science Department, Stillwell 426, Western Carolina University, Cullowhee, North Carolina 28723

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.

American Mathematical Society