R structures, Yang–Baxter equations, and related involution theorems

DOI10.1063/1.528333zbMath0689.35077OpenAlexW2003068044MaRDI QIDQ3031377

Walter Oevel

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1063/1.528333

zbMATH Keywords

Yang-Baxter equationKorteweg-de Vries equationLenard relationsLie bi-algebra

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Q99) Lie algebras and Lie superalgebras (17B99)

Related Items

R-matrices and higher Poisson brackets for integrable systems, Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization, Mastersymmetries, angle variables, and recursion operator of the relativistic Toda lattice, Algebraic structure of the gradient-holonomic algorithm for Lax integrable nonlinear dynamical systems. I, AKS hierarchy and bi-Hamiltonian geometry of Gelfand–Zakharevich type, Super-Toda lattices, R-matrix approach to lattice integrable systems, New integrable differential-difference and fractional nonlinear dynamical systems and their algebro-analytical properties, The bi-Hamiltonian structure of fully supersymmetric Korteweg-de Vries systems, Odd Hamiltonian structure for supersymmetric Sawada-Kotera equation, A new Liouville transformation for the Geng-Xue system, A reciprocal transformation for the Geng-Xue equation, On the construction of recursion operator and algebra of symmetries for field and lattice systems, Yang-Baxter equations and intermediate long wave hierarchies, Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems, Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators, On the simplectization of bi-Hamiltonian structures

Cites Work

• What is a classical r-matrix?
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• The Schouten bracket and Hamiltonian operators
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• A simple model of the integrable Hamiltonian equation
• EULER EQUATIONS ON FINITE-DIMENSIONAL LIE GROUPS