The linear SL_2(Z)-action on T^n: ergodic and von Neumann algebraic aspects
Abstract
The linear action of SL2(R) on Rn corresponding to its unique irreducible representation induces an action SL2(Z)↷Tn for every n⩾2 that factors through PSL2(Z) for n odd. Thus, setting Gn=SL2(Z) (respectively Gn=PSL2(Z)) for n even (respectively n odd), Gn↷Tn is free and ergodic, every ergodic sub-equivalence relation of the orbital equivalence relation is either amenable or rigid, and the fundamental group of the II1 factor Nn:=L∞(Tn)⋊Gn is trivial. For n even, L∞(Tn)⋊H is a maximal Haagerup subalgebra of Nn for every suitable maximal amenable subgroup H of SL2(Z).
Fields of Study & Subjects
Advanced Algebra and Geometry
Geometry and complex manifolds
Advanced Operator Algebra Research
Publication details
- Journal / source
- Journal of Operator Theory
- Publisher
- Theta Foundation
- Volume
- 95
- Issue
- 1
- Pages
- 3–20
- Publication date
- 1 March 2026