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arXiv · 2208.10157

Characterizing nilpotent Lie algebras that satisfy on converse of the Schur's theorem

A. Shamsaki·P. Niroomand
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Abstract

Let $ L $ be a finite dimensional nilpotent Lie algebra and $ d $ be the minimal number generators for $ L/Z(L). $ It is known that $ \dim L/Z(L)=d \dim L^{2}-t(L)$ for an integer $ t(L)\geq 0. $ In this paper, we classify all finite dimensional nilpotent Lie algebras $ L $ when $ t(L)\in \lbrace 0, 1, 2 \rbrace.$ We find also a construction, which shows that there exist Lie algebras of arbitrary $ t(L). $

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BibTeXRIS

A. Shamsaki, P. Niroomand. 2022-08-22. Characterizing nilpotent Lie algebras that satisfy on converse of the Schur's theorem. https://doi.org/10.1007/s13398-023-01448-0

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