Uniqueness Theorems for Twisted Steinberg Algebras

Given an ample Hausdorff groupoid $G$, a unital commutative ring $R$, and a discrete twist $(\mathrm{\Sigma },i,q)$, we establish a generalised uniqueness theorem for the twisted Steinberg algebra $A_R(G;\mathrm{\Sigma })$. 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 $A_R(G;\mathrm{\Sigma })$.