- journal article metadata
European Mathematical Society Publishing House
2017-06-29 23:45:01
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2017
2
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
Complete separable valued fields, probability measures on algebraic varieties, algebraic representations of amenable ergodic actions, Margulis–Zimmer super-rigidity
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].
Group theory and generalizations
Field theory and polynomials
Dynamical systems and ergodic theory
705
738
10.4171/GGD/413
http://www.ems-ph.org/doi/10.4171/GGD/413