Classification of constant solutions of the associative Yang-Baxter equation on \(\mathrm{Mat}_3\).

DOI10.1007/s11232-013-0096-zzbMath1291.16028arXiv1212.6421OpenAlexW1999391790MaRDI QIDQ2449539

Vladimir Sokolov

Publication date: 8 May 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.6421

zbMATH Keywords

Poisson bracketsassociative Yang-Baxter equationconstant solutions

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Applications of Lie algebras and superalgebras to integrable systems (17B80) Yang-Baxter equations (16T25)

Related Items (5)

On double Poisson structures on commutative algebras ⋮ Rota–Baxter operators of nonzero weight on the matrix algebra of order three ⋮ Rota-Baxter operators of nonzero weight on a complete linear Lie algebra of order two ⋮ Double quasi-Poisson brackets: fusion and new examples ⋮ Rota-Baxter operators on unital algebras

Cites Work

• Unnamed Item
• Bi-Hamiltonian ordinary differential equations with matrix variables
• Frobenius Lie algebras
• The invariant theory of \(n\times n\) matrices
• Integrable ODEs on associative algebras
• Parameter-dependent associative Yang–Baxter equations and Poisson brackets
• Double Poisson algebras
• On the associative analog of Lie bialgebras

This page was built for publication: Classification of constant solutions of the associative Yang-Baxter equation on \(\mathrm{Mat}_3\).