Elements of a Lie algebra acting nilpotently in all its representations

2022/09/27 by O. G. Styrt, Styrt, O. G.
Mathematics · #17B10 #17B20 #17B30 #17B40 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2209.13309

openalex publication_date 2022/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An equivalent condition for an element of a Lie algebra acting nilpotently in all its representations is obtained. Namely, it should belong to the derived algebra and go via factoring over the radical to a nilpotent element of the corresponding (semisimple) quotient algebra.

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