Tracial states on groupoid $C^{\ast }$-algebras and essential freeness

Kang Li, Jiawen Zhang

Let $\mathcal{G}$ be a locally compact Hausdorff étale groupoid. We call a tracial state $\tau$ on a general groupoid $C^{\ast }$-algebra $C_{\nu }^{\ast }(\mathcal{G})$ canonical if $τ=τ|_{C_0(\mathc…