Integrable matrix equations related to pairs of compatible associative algebras

DOI10.1088/0305-4470/39/40/011zbMath1146.17313arXivmath/0604574OpenAlexW3105591247MaRDI QIDQ3418410

Vladimir Sokolov, Alexander Odesskii

Publication date: 5 February 2007

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604574

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relationships between algebraic curves and integrable systems (14H70) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (17)

R-matrix, Lax pair, and multiparameter decompositions of Lie algebras ⋮ Bi-Hamiltonian ordinary differential equations with matrix variables ⋮ The category and operad of matching dialgebras ⋮ Universal central extensions of compatible Leibniz algebras ⋮ Homotopy transfer theorem for linearly compatible di-algebras ⋮ Totally compatible associative and Lie dialgebras, tridendriform algebras and PostLie algebras ⋮ Bi-Hamiltonian structures and singularities of integrable systems ⋮ Pairs of compatible associative algebras, classical Yang-Baxter equation and quiver representations ⋮ Completeness of commutative Sokolov-Odesskii subalgebras and Nijenhuis operators on ⋮ Completeness of some commutative subalgebras associated with Nijenhuis operators on Lie algebras ⋮ Algebraic properties of compatible Poisson brackets ⋮ Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras ⋮ Noncommutative extensions of elliptic integrable Euler–Arnold tops and Painlevé VI equation ⋮ Nijenhuis geometry ⋮ Invariant Nijenhuis tensors and integrable geodesic flows ⋮ A class of integrable flows on the space of symmetric matrices ⋮ TWISTED COMMUTING SQUARES

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