Compactness of minimal closed invariant sets of actions of unipotent groups (Q810157)

Let G be a connected Lie group and \(\Gamma\) a lattice in G, i.e. a discrete subgroup with finite covolume. Let U be an Ad-unipotent subgroup of G, i.e. Ad u is a unipotent linear map for every \(u\in U\). The group U acts on G/\(\Gamma\) by left translations. A closed U-invariant subset \(X\subset G/\Gamma\) is called minimal if Ux is dense in X for every \(x\in X\). The author proves that every minimal closed U-invariant subset X of G/\(\Gamma\) is compact.