Cartan subalgebras for non-principal twisted groupoid $C^{\ast }$-algebras

Anna Duwenig, Elizabeth Gillaspy, Rachael Norton +2

Renault proved in 2008 that if $G$ is a topologically principal groupoid, then $C_0(G^{(0)})$ is a Cartan subalgebra in $C_r^{\ast }(G,\Sigma )$ for any twist $\Sigma$ over $G$. However, there are…