Complete commutative subalgebras in polynomial poisson algebras: a proof of the Mischenko-Fomenko conjecture
journal contributionposted on 2017-01-10, 11:36 authored by Alexey BolsinovAlexey Bolsinov
The Mishchenko–Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra g there exists a complete set of commuting polynomials on its dual space g*. In terms of the theory of integrable Hamiltonian systems this means that the dual space g* endowed with the standard Lie–Poisson bracket admits polynomial integrable Hamiltonian systems. This conjecture was proved by S. T. Sadetov in 2003. Following his idea, we give an explicit geometric construction for commuting polynomials on g* and consider some examples.
- Mathematical Sciences
Published inTheoretical and Applied Mechanics
CitationBOLSINOV, A., 2016. Complete commutative subalgebras in polynomial poisson algebras: a proof of the Mischenko-Fomenko conjecture. Theoretical and Applied Mechanics [= Teorijska i primenjena mehanika], 43 (2), pp.145-168.
PublisherSerbian Society of Mechanics
- AM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis paper is a revised version of: BOLSINOV, A.V., 2006. Complete commutative families of polynomials in Poisson-Lie algebras: a proof of the Mischenko-Fomenko conjecture. Trudy seminara po vektornomu i tenzornomu analizu (ISSN: 0373-4870), 26, pp.87-109.