Non-strong ergodicity of canonical actions of the Thompson groups

2025/10/15 by Arimoto, Ryoya
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2510.13309

Abstract

We show that the canonical actions of the Thompson group V and its generalizations on the Cantor set are not strongly ergodic. This implies that the associated crossed product von Neumann algebras are not full. This also yields a non-embedding result for the Thompson groups.

Citations

• The regular representation of Neretin groups is factorial
• Generalisations of Thompson's group V arising from purely infinite groupoids
• Non-inner amenability of the Higman-Thompson groups
• A brief introduction to amenable equivalence relations
• Non-inner amenability of the Thompson groups T and V
• Topological full groups of one-sided shifts of finite type

Related

• The von Neumann Algebra of the Canonical Equivalence Relation of the Generalized Thompson Group
• On solid ergodicity for Gaussian actions
• Free products in R. Thompson's group V
• Non-inner amenability of the Thompson groups T and V
• Relatively amenable actions of Thompson's groups