What question did this study set out to answer?

The goal is to explore the characteristics of closed subsemigroups within simply connected nilpotent Lie groups.

March 29, 2026Open Access

Subsemigroups of Nilpotent Lie Groups

Key Points

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 .

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