Comparison and Simplicity of Commutator Subgroups of Full Groups

2020/11/02 by Hung-Chang Liao, Liao, Hung-Chang
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2011.01176

openalex publication_date 2020/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On Groups of Measure Preserving Transformations. I
• Étale groupoids and their C^*-algebras
• 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^*-algebras

Related

• Some remarks on topological full groups of Cantor minimal systems II
• Topological full groups of etale groupoids
• Simplicity of algebras associated to étale groupoids
• A dichotomy for topological full groups
• Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems