Twisting of Lie triple systems, $L_\infty$-algebras, and (generalized) matched pairs

Jia Zhao; Haobo Xia

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arXiv · 2406.10596

Twisting of Lie triple systems, $L_\infty$-algebras, and (generalized) matched pairs

Jia Zhao·Haobo Xia

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Abstract

In this paper, we introduce notions of (proto-, quasi-)twilled Lie triple systems and give their equivalent descriptions using the controlling algebra and bidegree convention. Then we construct an $L_\infty$-algebra via a twilled Lie triple system. Besides, we establish the twisting theory of Lie triple systems and then characterize the twisting as a Maurer-Cartan element in the constructed $L_\infty$-algebra. Finally, we clarify the relationship between twilled Lie triple systems and matched pairs and clarify the relationship between twilled Lie triple systems and relative Rota-Baxter operators respectively so that we obtain the relationship between matched pairs of Lie triple systems and relative Rota-Baxter operators.

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Jia Zhao, Haobo Xia. 2024-06-15. Twisting of Lie triple systems, $L_\infty$-algebras, and (generalized) matched pairs. https://arxiv.org/abs/2406.10596

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