Non-strong ergodicity of canonical actions of the Thompson groups
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Journal of the Mathematical Society of Japan
- Volume
- -1
- Issue
- -1
- Publication date
- 15 July 2026