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, 2026Journal of Lie theoryOpen Access

Subsemigroups of Nilpotent Lie Groups

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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.

Implication

This analysis proves characterizations of subsemigroups in nilpotent Lie groups, suggesting structural properties.

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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Cite This Study

Abels et al. (2020) studied this question.

synapsesocial.com/papers/69c8c115de0f0f753b39baa2 https://doi.org/10.5802/jolt.1109

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Implication

This analysis proves characterizations of subsemigroups in nilpotent Lie groups, suggesting structural properties.

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 .

Subsemigroups of Nilpotent Lie Groups

Key Points

Implication

Abstract

Discussion

Cite This Study

Subsemigroups of Nilpotent Lie Groups

Key Points

Implication

Abstract

Discussion

Cite This Study

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