Locally Unitary Groupoid Crossed Products

Details Locally Unitary Groupoid Crossed Products Locally Unitary Groupoid Crossed Products

2009-08-26

arxiv.org/abs/0908.3806v1

Mathematics

Operator Algebras

25 pages

Scientific paper

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 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.

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