1. Simplicity criteria for etale groupoid $C^*$-algebras
- Author
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Crytser, Danny and Nagy, Gabriel
- Subjects
Mathematics - Operator Algebras ,46L35 - Abstract
We develop a framework suitable for obtaining simplicity criteria for reduced $C^*$-algebras of Hausdorff etale groupoids. This is based on the study of certain non-degenerate $C^*$-subalgebras (in the case of groupoids, the $C^*$-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 $C^*$-algebras by discrete groups., Comment: 37 pages, revised version of arXiv:1805.11173 (minor typo fixes and changes in title, exposition and terminology)
- Published
- 2018