Locally unitary groupoid crossed products

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Abstract

We define the notion of a principal S-bundle where S is a groupoid group bundle and show that there is a one-to-one correspondence between principal S-bundles and elements of a sheaf cohomology group associated to S. We also define the notion of a locally unitary action and show that the spectrum of the crossed product is a principal Ŝ-bundle. Furthermore, we prove that the isomorphism class of the spectrum determines the exterior equivalence class of the action and that every principal bundle can be realized as the spectrum of some locally unitary crossed product.

Original languageEnglish (US)
Pages (from-to)411-442
Number of pages32
JournalIndiana University Mathematics Journal
Volume60
Issue number2
DOIs
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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