JournalsggdVol. 11, No. 2pp. 705–738

Almost algebraic actions of algebraic groups and applications to algebraic representations

  • Uri Bader

    Technion, Haifa, Israel
  • Bruno Duchesne

    Université de Lorraine, Vandœuvre-lès-Nancy, France
  • Jean Lécureux

    Université Paris-Sud 11, France
Almost algebraic actions of algebraic groups and applications to algebraic representations cover
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Abstract

Let GG be an algebraic group over a complete separable valued field kk. We discuss the dynamics of the GG-action on spaces of probability measures on algebraic GG-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].

Cite this article

Uri Bader, Bruno Duchesne, Jean Lécureux, Almost algebraic actions of algebraic groups and applications to algebraic representations. Groups Geom. Dyn. 11 (2017), no. 2, pp. 705–738

DOI 10.4171/GGD/413