PUB - Publikationen an der Universität Bielefeld

Let S be a subsemigroup of a simply connected nilpotent Lie group G. We construct an asymptotic semigroup S-0 in the associated graded Lie group G(0) of G. We can compute the image of S-0 in the abelianization G(0)(ab) = G(ab). This gives useful information about S. As an application, we obtain a transparent proof of the following result of E. B. Vinberg and the author: either there is an epimorphism f : G -> R such that f (s) >= 0 for every s in S or the closure (S) over bar of S is a subgroup of G and G/(S) over bar is compact.