Simplicity criteria for etale groupoid $C^{\ast }$-algebras

Abstract

We develop a framework suitable for obtaining simplicity criteria for reduced $C^{\ast }$-algebras of Hausdorff etale groupoids. This is based on the study of certain non-degenerate $C^{\ast }$-subalgebras (in the case of groupoids, the $C^{\ast }$-algebra of the interior isotropy bundle), for which one can control (non-unique) state extensions to the ambient C*-algebra. As an application, we give simplicity criteria for reduced crossed products of abelian $C^{\ast }$-algebras by discrete groups.

37 pages, revised version of arXiv:1805.11173 (minor typo fixes and changes in title, exposition and terminology)