$C^{\ast }$-uniqueness Results for Groupoids

Abstract

For a second-countable locally compact Hausdorff étale groupoid $\mathcal{G}$ with a continuous $2$-cocycle $\sigma$ we find conditions that guarantee that ${\ell }^1(\mathcal{G},\sigma )$ has a unique $C^{\ast }$-norm.

arXiv comment13 pages. Comments welcome

References in corpus (4)

• Étale groupoids and their $C^{\ast }$-algebras
• A non-amenable groupoid whose maximal and reduced $C^{\ast }$-algebras are the same
• Non-amenable principal groupoids with weak containment
• Uniqueness questions for C*-norms on group rings