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arXiv · 2310.19490

From $\mathcal{O}$-operators of 3-Dimensional 3-Lie algebras to 3-Pre-Lie algebras

Cheng Ziying·Kang Chuangchuang·Lü Jiafeng
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Abstract

In this paper, we explicitly determine all $\mathcal{O}$-operators with respect to the adjoint representation of 3-dimensional complex 3-Lie algebras. Furthermore, we provide the induced 3-Pre-Lie algebra structures and the corresponding solutions of the 3-Lie classical Yang-Baxter equation in the 6-dimensional 3-Lie algebras $A\ltimes_{\mathrm{ad}^*} A^*$.

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Cheng Ziying, Kang Chuangchuang, Lü Jiafeng. 2023-10-30. From $\mathcal{O}$-operators of 3-Dimensional 3-Lie algebras to 3-Pre-Lie algebras. https://arxiv.org/abs/2310.19490

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