Skew-symmetric solutions of the classical Yang-Baxter equation and $\mathcal{O}$-operators of Malcev algebras Article Swipe

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YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2402.08489

We study connections between skew-symmetric solutions of the classical Yang-Baxter equation (CYBE) and $\mathcal{O}$-operators of Malcev algebras. We prove that a skew-symmetric solution of the CYBE on a Malcev algebra can be interpreted as an $\mathcal{O}$-operator associated to the coadjoint representation. We show that this connection can be enhanced with symplectic forms when considering non-degenerate skew-symmetric solutions. We also show that $\mathcal{O}$-operators associated to a general representation could give skew-symmetric solutions of the CYBE on certain semi-direct products of Malcev algebras. We reveal the relationship between invertible $\mathcal{O}$-operators and compatible pre-Malcev algebra structures on a Malcev algebra. We finally obtain several analogous results on connections between the CYBE and $\mathcal{O}$-operators in the case of pre-Malcev algebras.

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Skew Mathematics Pure mathematics Mathematical physics Physics Astronomy

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2402.08489
PDF: https://arxiv.org/pdf/2402.08489
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4391871277

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DOI: https://doi.org/10.48550/arxiv.2402.08489

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Title: Skew-symmetric solutions of the classical Yang-Baxter equation and $\mathcal{O}$-operators of Malcev algebras

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-02-13

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Authors: Shan Ren, Runxuan Zhang

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Landing page: https://arxiv.org/abs/2402.08489

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PDF URL: https://arxiv.org/pdf/2402.08489

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Concepts: Skew, Mathematics, Pure mathematics, Mathematical physics, Physics, Astronomy

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