Local derivations and automorphisms of nilpotent Lie algebra

2024/05/07 by Abror Khudoyberdiyev, Khudoyberdiyev, Abror, Doston Jumaniyozov +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2405.04209

openalex publication_date 2024/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is devoted to the study of local derivations and automorphisms of nilpotent Lie algebras. Namely, we proved that nilpotent Lie algebras with indices of nilpotency 3 and 4 admit local derivation (local automorphisms) which is not a derivation (automorphisms). Further, it is presented a sufficient condition under which a nilpotent Lie algebra admits a local derivation which is not a derivation. With the same condition, it is proved the existence of pure local automorphism on a nilpotent Lie algebra. Finally, we present an n-dimensional non-associative algebra for which the space of local derivations coincides with the space of derivations.

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