Groupoid equivalence and the associated iterated crossed product

Abstract

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

18 pages; changed typo in title

References in corpus (2)

• Renault's Equivalence Theorem for Groupoid Crossed Products
• The Brauer Semigroup of a groupoid and a symmetric imprimitivity theorem