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arXiv · 2610.40348

Local Derivations and Local Automorphisms of Arbitrary Finite-Dimensional Nilpotent Lie and Leibniz Algebras

Khusainboy Atajonov·Abror Khudoyberdiyev·Bakhtiyor Yusupov
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Abstract

We study local derivations and local automorphisms of finite-dimensional nilpotent complex Lie and right Leibniz algebras. We prove that every non-abelian Lie algebra in this class admits both a local derivation which is not a derivation and a local automorphism which is not an automorphism. The constructions use a derivation $D$ satisfying $0\ne D([L,L])\subseteq Z(L)$. For non-abelian right Leibniz algebras, both existence statements hold whenever the dimension is at most seven or the nilpotency class is at most four. We construct an eight-dimensional non-Lie algebra of class five satisfying $\LocDer(A)=\Der(A)$ and $\LocAut(A)=\Aut(A)$. Consequently, eight and five are the least possible dimension and nilpotency class, respectively, for either equality.

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Khusainboy Atajonov, Abror Khudoyberdiyev, Bakhtiyor Yusupov. 2026-10-29. Local Derivations and Local Automorphisms of Arbitrary Finite-Dimensional Nilpotent Lie and Leibniz Algebras. https://arxiv.org/abs/2610.40348

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