The brauer semigroup of a groupoid and a symmetric imprimitivity theorem

Jonathan Henry Brown, Geoff Goehle

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1943-1972
Number of pages30
JournalTransactions of the American Mathematical Society
Volume366
Issue number4
DOIs
StatePublished - Jan 30 2014

Fingerprint

Equivalence classes
Groupoid
Morita Equivalence
Semigroup
Equivalence class
Isomorphism
Theorem
Brauer Group
Dynamical systems
Transformation group
Crossed Product
Locally Compact
Monoid
Equivariant
Dynamical system
Equivalence
Generalise

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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The brauer semigroup of a groupoid and a symmetric imprimitivity theorem. / Brown, Jonathan Henry; Goehle, Geoff.

In: Transactions of the American Mathematical Society, Vol. 366, No. 4, 30.01.2014, p. 1943-1972.

Research output: Contribution to journalArticle

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