A Note on Derivations of Lie Algebras

2010/11/07 by M. Shahryari, Shahryari, Mohammad
Mathematics · #17B40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1011.1609

openalex publication_date 2010/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we will prove that a finite dimensional Lie algebra L of characteristic zero, admitting an abelian algebra of derivations D≤ Der(L) with the property Lⁿ⊆ ∑_{d∈ D}d(L) for some n≥ 1, is necessarily solvable. As a result, if L has a derivation d:L→ L, such that Lⁿ⊆ d(L), for some n≥ 1, then L is solvable.

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