On Kirillov's lemma for nilpotent Lie algebras
Ingrid Beltita, Daniel Beltita
TL;DR
This paper refines Kirillov's lemma for nilpotent Lie algebras with a 1-dimensional center and explores the structural properties of 3-step nilpotent Lie algebras.
Contribution
It provides a sharper version of Kirillov's lemma and applies it to analyze the structure of 3-step nilpotent Lie algebras.
Findings
Sharpened version of Kirillov's lemma for specific nilpotent Lie algebras
Structural insights into 3-step nilpotent Lie algebras
Potential applications to representation theory
Abstract
We establish a sharpening of Kirillov's lemma on nilpotent Lie algebras with 1-dimensional center and use it to study the structure of 3-step nilpotent Lie algebras.
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