Complete commutative subalgebras in polynomial poisson algebras: A proof of the Mischenko-Fomenko conjecture

DOI10.2298/TAM161111012BzbMath1474.37065arXiv1206.3882WikidataQ123094673 ScholiaQ123094673MaRDI QIDQ4986495

Alexei V. Bolsinov

Publication date: 27 April 2021

Published in: Theoretical and Applied Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.3882

zbMATH Keywords

complete integrabilityfield extensionPoisson-Lie bracketchains of subalgebrasMischenko-Fomenko conjectureshifting of argument

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Poisson manifolds; Poisson groupoids and algebroids (53D17) Applications of Lie algebras and superalgebras to integrable systems (17B80) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Poisson algebras (17B63) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Related Items (6)

Integrable systems associated to the filtrations of Lie algebras ⋮ Two Integrable Cases of a Ball Rolling over a Sphere in $\mathbb{R}^n$ ⋮ Almost multiplicity free subgroups of compact Lie groups and polynomial integrability of sub-Riemannian geodesic flows ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Open problems in the theory of finite-dimensional integrable systems and related fields ⋮ Invariant Nijenhuis tensors and integrable geodesic flows

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