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arXiv · 2301.12953

The $ω$-Lie algebra defined by the commutator of an $ω$-left-symmetric algebra is not perfect

Zhiqi Chen·Junna Ni·Jianhua Yu
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Abstract

In this paper, we study admissible $ω$-left-symmetric algebraic structures on $ω$-Lie algebras over the complex numbers field $\mathbb C$. Based on the classification of $ω$-Lie algebras, we prove that any perfect $ω$-Lie algebra can't be the $ω$-Lie algebra defined by the commutator of an $ω$-left-symmetric algebra.

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Zhiqi Chen, Junna Ni, Jianhua Yu. 2022-09-30. The $ω$-Lie algebra defined by the commutator of an $ω$-left-symmetric algebra is not perfect. https://arxiv.org/abs/2301.12953

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