Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras

Haiying Li; Tianshui Ma

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arXiv · 2502.18717

Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras

Haiying Li·Tianshui Ma

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Abstract

In this paper the conditions that when a Lie algebra is Nijenhuis are investigated. Furthermore all the Nijenhuis operators on $\mathfrak{sl}_2$ under the standard Cartan-Weyl basis are given. On the other hand, the relations between the classical Yang-Baxter equation and Nijenhuis operators $N$ on a Lie algebra and $P$ on a Lie coalgebra are derived by means of the bialgebraic theory for Nijenhuis Lie algebras.

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Haiying Li, Tianshui Ma. 2025-02-26. Classical Yang-Baxter equations and Nijenhuis operators for Lie algebras. https://arxiv.org/abs/2502.18717

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