Uniqueness Theorems for Twisted Steinberg Algebras

Abstract

Given an ample Hausdorff groupoid $G$, a unital commutative ring $R$, and a discrete twist $(\Sigma,i,q)$, we establish a generalised uniqueness theorem for the twisted Steinberg algebra $A_R(G;\Sigma)$. By applying this theorem when $G$ is effective, we establish a Cuntz-Krieger uniqueness theorem as a corollary. We also prove a generalised graded uniqueness theorem for $A_R(G;\Sigma)$.