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

Abstract

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.

Cited by in corpus (13)

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• On double Poisson structures on commutative algebras
• Spectrum of Rota-Baxter operators
• Double quasi-Poisson brackets : fusion and new examples
• Rota-Baxter operators of weight zero on upper-triangular matrices of order three
• Anti-Frobenius Algebras and Associative Yang-Baxter Equation
• Rota-Baxter operators of weight zero on the matrix algebra of order three without unit in kernel
• An example of a simple double Lie algebra
• Rota-Baxter operators of nonzero weight on the split Cayley-Dickson algebra
• Rota-Baxter operators on the simple Jordan algebra of matrices of order two
• Rota-Baxter operators of nonzero weight on the matrix algebra of order three
• Double Lie algebras of a nonzero weight
• Shifted double Lie-Rinehart algebras