Almost algebraic actions of algebraic groups and applications to algebraic representations
Group Theory
2021-02-03 v3
Abstract
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 due to Bader and Furman.
Cite
@article{arxiv.1411.5327,
title = {Almost algebraic actions of algebraic groups and applications to algebraic representations},
author = {Uri Bader and Bruno Duchesne and Jean Lécureux},
journal= {arXiv preprint arXiv:1411.5327},
year = {2021}
}
Comments
Correction of a small mistake in Proposition 5.3