Geodesic
Almost algebraic actions of algebraic groups and applications to algebraic representations
Uri Bader1 orcid ; Bruno Duchesne2 ; Jean Lécureux3 orcid
1Technion, Haifa, Israel
2Université de Lorraine, Vandœuvre-lès-Nancy, France
3Université Paris-Sud 11, France
Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 705-738

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DOI

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].
DOI : 10.4171/ggd/413
Classification : 20-XX, 12-XX, 37-XX
Mots-clés : Complete separable valued fields, probability measures on algebraic varieties, algebraic representations of amenable ergodic actions, Margulis–Zimmer super-rigidity

Uri Bader  1   ; Bruno Duchesne  2   ; Jean Lécureux  3

1 Technion, Haifa, Israel
2 Université de Lorraine, Vandœuvre-lès-Nancy, France
3 Université Paris-Sud 11, France 
Uri Bader; Bruno Duchesne; Jean Lécureux. Almost algebraic actions of algebraic groups and applications to algebraic representations. Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 705-738. doi: 10.4171/ggd/413
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     title = {Almost algebraic actions of algebraic groups and applications to algebraic representations},
     journal = {Groups, geometry, and dynamics},
     pages = {705--738},
     year = {2017},
     volume = {11},
     number = {2},
     doi = {10.4171/ggd/413},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/413/}
}
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