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arXiv · 1206.2066

Groupoid equivalence and the associated iterated crossed product

Jonathan Henry Brown·Geoff Goehle·Dana P. Williams
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Abstract

Given groupoids $G$ and $H$ and a $(G,H)$-equivalence $X$ we may form the transformation groupoid $G\ltimes X\rtimes H$. Given a separable groupoid dynamical system $(A,G\ltimes X\rtimes H,ω)$ we may restrict $ω$ to an action of $G\ltimes X$ on $A$ and form the crossed product $A\rtimes G\ltimes X$. We show that there is an action of $H$ on $A\rtimes G\ltimes X$ and that the iterated crossed product $(A\rtimes G\ltimes X)\rtimes H$ is naturally isomorphic to the crossed product $A\rtimes (G\ltimes X\rtimes H)$.

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Jonathan Henry Brown, Geoff Goehle, Dana P. Williams. 2012-07-24. Groupoid equivalence and the associated iterated crossed product. https://arxiv.org/abs/1206.2066

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