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

preprint2012arXivOpen access

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

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

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