Comparison and Simplicity of Commutator Subgroups of Full Groups

Abstract

We show that for a minimal, second countable, locally compact Hausdorff étale groupoid whose unit space is homeomorphic to the Cantor set, if the groupoid has comparison then the commutator subgroup of its full group is simple. This generalizes a result of Bezuglyi and Medynets for Cantor minimal systems and complements Matui's results for topological full groups.

arXiv comment15 pages

References in corpus (5)

• Étale groupoids and their $C^{\ast }$-algebras
• Almost finiteness for general etale groupoids and its applications to stable rank of crossed products
• The comparison property of amenable groups
• The type semigroup, comparison and almost finiteness for ample groupoids
• Purely infinite locally compact Hausdorff étale groupoids and their $C^{\ast }$-algebras