Locally unitary groupoid crossed products
Geoff Goehle
47L6522A22groupoidscrossed products
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 $\hat{S}$-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.
Indiana University Mathematics Journal
2011
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10.1512/iumj.2011.60.4143
10.1512/iumj.2011.60.4143
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Indiana Univ. Math. J. 60 (2011) 411 - 442
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