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arXiv · 2503.11595

Generalized derivations of $\omega$-Lie algebras

Yin Chen·Shan Ren·Jiawen Shan·Runxuan Zhang
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Abstract

This article explores the structure theory of compatible generalized derivations of finite-dimensional $\omega$-Lie algebras over a field $\mathbb{K}$. We prove that any compatible quasiderivation of an $\omega$-Lie algebra can be embedded as a compatible derivation into a larger $\omega$-Lie algebra, refining the general result established by Leger and Luks in 2000 for finite-dimensional nonassociative algebras. We also provide an approach to explicitly compute (compatible) generalized derivations and quasiderivations for all $3$-dimensional non-Lie complex $\omega$-Lie algebras.

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Yin Chen, Shan Ren, Jiawen Shan, Runxuan Zhang. 2025-03-14. Generalized derivations of $\omega$-Lie algebras. https://doi.org/10.1142/s0219498826502063

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