On nilpotent generators of the symplectic Lie algebra

2019/08/12 by Chistopolskaya, Alisa · 1 citation
#17B05 #17B22 (Primary) 15A04 (Secondary) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1908.04065

Abstract

Let \mathfraksp_2n(\mathbb K) be the symplectic Lie algebra over an algebraically closed field of characteristic zero. We prove that for any nonzero nilpotent element X ∈ \mathfraksp_2n(\mathbb K) there exists a nilpotent element Y ∈ \mathfraksp_2n(\mathbb K) such that X and Y generate \mathfraksp_2n(\mathbb K).

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