Almost algebraic actions of algebraic groups and applications to algebraic representations

Uri Bader, Bruno Duchesne, Jean Lécureux

Research output: Contribution to journalArticlepeer-review


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 ofMargulis-Zimmer super-rigidity phenomenon [2].

Original languageEnglish
Pages (from-to)705-738
Number of pages34
JournalGroups, Geometry, and Dynamics
Issue number2
StatePublished - 2017


  • Algebraic representations of amenable ergodic actions
  • Complete separable valued fields
  • Margulis-Zimmer super-rigidity
  • Probability measures on algebraic varieties

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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