Nilpotent groups with primitive ideal spaces
In this article we study non-abelian extensions of a Lie group modeled on a locally convex space by a Lie group . The equivalence classes of such extension are grouped into those corresponding to a class of so-called smooth outer actions of on . If is given, we show that the corresponding set of extension classes is a principal homogeneous space of the locally smooth cohomology group . To each a locally smooth obstruction class in a suitably defined cohomology group is defined....
We prove that there exists a non-abelian group structure on the Urysohn universal metric space. More precisely, we introduce a variant of the Graev metric that enables us to construct a free group with countably many generators equipped with a two-sided invariant metric that is isometric to the rational Urysohn space. We list several related open problems.
We obtain upper and lower estimates for the Green function for a second order noncoercive differential operator on a homogeneous manifold of negative curvature.