Superrigid Subgroups and Syndetic Hulls in Solvable Lie Groups
It is not difficult to see that every group homomorphism from ℤ k to ℝ n extends to a homomorphism from ℝ k to ℝ n . We discuss other examples of discrete subgroups Γ of connected Lie groups G, such that the homomorphisms defined on Γ can (“virtually”) be extended to homomorphisms defined on all of G. For the case where G is solvable, we give a simple proof that Γ has this property if it is Zariski dense. The key ingredient is a result on the existence of syndetic hulls.