Algebraic and geometric properties of quadratic Hamiltonians determined by sectional operators

DOI10.1134/S0001434611110058zbMath1317.37068MaRDI QIDQ2435858

Andrey Yu. Konyaev, Alexei V. Bolsinov

Publication date: 20 February 2014

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Poisson bracketcoadjoint representationsemi-simple Lie algebraFrobenius Lie algebrafinite-dimensional Lie algebrasectional operatorbi-Hamiltonian Euler equationintegrable Euler equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65)

Related Items (3)

Algebraic geometry and stability for integrable systems ⋮ Finite-dimensional integrable systems: a collection of research problems ⋮ Argument shift method and sectional operators: applications to differential geometry

Cites Work

• A formal Frobenius theorem and argument shift
• Analytic classification of pairs of involutions and its applications
• Generalized Liouville method of integration of Hamiltonian systems
• A Fubini theorem for pseudo-Riemannian geodesically equivalent metrics
• Invariants of real low dimension Lie algebras
• Integrable Hamiltonian systems on low-dimensional Lie algebras
• Lie Group Representations on Polynomial Rings
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Algebraic and geometric properties of quadratic Hamiltonians determined by sectional operators