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arxiv: 1212.6421 · v1 · pith:WCFCIPNBnew · submitted 2012-12-27 · 🌊 nlin.SI

Classification of constant solutions for associative Yang-Baxter equation on gl(3)

V. Sokolov This is my paper
classification 🌊 nlin.SI
keywords associativeclassificationconstantequationpoissonsolutionsyang-baxteralgebra
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We find all non-equivalent constant solutions for classical associative Yang-Baxter equation for $gl(3)$. New examples found in the classification yield the corresponding quadratic trace Poisson brackets, double Poisson structures on free associative algebra with three generators and anti-Frobenius associative algebras.

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  1. Coupled double Poisson brackets

    math.QA 2026-05 unverdicted novelty 7.0

    Introduces coupled double Poisson brackets, proves bijection to wheeled Poisson brackets, and gives correspondences to Poisson-left-pre-Lie algebras and Yang-Baxter solutions on free polynomial algebras.