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

Zhiqi Chen; Junna Ni; Jianhua Yu

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arXiv · 2301.12953

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

Zhiqi Chen·Junna Ni·Jianhua Yu

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Abstract

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

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

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