The goal is to explore the characteristics of closed subsemigroups within simply connected nilpotent Lie groups.
Analyzed properties of closed subsemigroups in the context of nilpotent Lie groups.
Utilized group theory and epimorphism concepts to establish structural relationships.
Demonstrated that closed subsemigroups are either subgroups or relate through specific epimorphisms.
Confirmed the existence of an epimorphism f from G to R satisfying f(s) > 0 for all s in S.
Abstract
For a closed subsemigroup S of a simply connected nilpotent Lie group G , we prove that either S is a subgroup, or there is an epimorphism f : G R such that f (s) 0 for all s S .