Groups, Geometry, and Dynamics


Full-Text PDF (372 KB) | Metadata | Table of Contents | GGD summary
Volume 11, Issue 2, 2017, pp. 705–738
DOI: 10.4171/GGD/413

Published online: 2017-06-26

Almost algebraic actions of algebraic groups and applications to algebraic representations

Uri Bader[1], Bruno Duchesne[2] and Jean Lécureux[3]

(1) Technion, Haifa, Israel
(2) Université de Lorraine, Vandœuvre-lès-Nancy, France
(3) Université Paris-Sud 11, France

Let $G$ be an algebraic group over a complete separable valued field $k$. We discuss the dynamics of the $G$-action on spaces of probability measures on algebraic $G$-varieties. We show that the stabilizers of measures are almost algebraic and the orbits are separated by open invariant sets. We discuss various applications, including existence results for algebraic representations of amenable ergodic actions. The latter provides an essential technical step in the recent generalization of Margulis–Zimmer super-rigidity phenomenon [2].

Keywords: Complete separable valued fields, probability measures on algebraic varieties, algebraic representations of amenable ergodic actions, Margulis–Zimmer super-rigidity

Bader Uri, Duchesne Bruno, Lécureux Jean: Almost algebraic actions of algebraic groups and applications to algebraic representations. Groups Geom. Dyn. 11 (2017), 705-738. doi: 10.4171/GGD/413