Groupoid algebras as covariance algebras

Abstract

Suppose $\mathcal{G}$ is a second-countable locally compact Hausdorff étale groupoid, $G$ is a discrete group containing a unital subsemigroup $P$, and $c:\mathcal{G}\to G$ is a continuous cocycle. We derive conditions on the cocycle such that the reduced groupoid $C^{\ast }$-algebra $C_r^{\ast }(\mathcal{G})$ may be realised naturally as the covariance algebra of a product system over $P$ with coefficient algebra $C_r^{\ast }(c^{-1}(e))$. When $(G,P)$ is a quasi-lattice ordered group, we also derive conditions that allow $C_r^{\ast }(\mathcal{G})$ to be realised as the Cuntz--Nica--Pimsner algebra of a compactly aligned product system.

30 pages

References in corpus (1)

• C*-algebras associated to product systems of Hilbert bimodules

Cited by in corpus (1)

• Strongly graded groupoid and directed graph algebras