Par : Lectures on the Stück–Zimmer Theorem | Notes

Lectures on the Stück–Zimmer Theorem | Notes — Thu, 14 Jun 2018 14:39:42 +0000

[…] Note that all examples above are ergodic, but none is properly ergodic, that is all are supported on a single conjugacy class. Properly ergodic IRSs do exist in some groups. The constructions above show that whenever a lcsc group ( G ) either is not simple, or has a proper nontrivial cofinite subgroup it has IRSs beyong the « trivial » ones ( delta_G ) and ( delta_{mathrm{Id}} ). There are discrete (Thompson groups) and non-discrete (see Adrien le Boudec’s talk) examples of totally disconnected groups where these are the only ergodic IRSs. There is however no known example of a nondiscrete, compactly generated group where this propert of « non nontrivial IRSs » holds. A candidate for this is the Neretin group, which we discuss in another series of lectures. […]

Commentaires sur : The Neretin groups (Bruno Duchesne)

Par : Lectures on the Stück–Zimmer Theorem | Notes