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arXiv · 1910.01472

Representations of $\omega$-Lie Algebras and Tailed Derivations of Lie Algebras

Runxuan Zhang
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Abstract

We study the representation theory of finite-dimensional $\omega$-Lie algebras over the complex field. We derive an $\omega$-Lie version of the classical Lie's theorem, i.e., any finite-dimensional irreducible module of a soluble $\omega$-Lie algebra is one-dimensional. We also prove that indecomposable modules of some three-dimensional $\omega$-Lie algebras could be parametrized by the complex field and nilpotent matrices. We introduce the notion of a tailed derivation of a nonassociative algebra $g$ and prove that if $g$ is a Lie algebra, then there exists a one-to-one correspondence between tailed derivations of $g$ and one-dimensional $\omega$-extensions of $g$.

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Runxuan Zhang. 2019-10-03. Representations of $\omega$-Lie Algebras and Tailed Derivations of Lie Algebras. https://arxiv.org/abs/1910.01472

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