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

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posted on 10.01.2017, 11:36 by Alexey 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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Theoretical and Applied Mechanics

Citation

BOLSINOV, 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.

Publisher

Serbian Society of Mechanics

Version

AM (Accepted Manuscript)

Publisher statement

This 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/

Publication date

2016

Notes

This 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.

ISSN

1450-5584

Language

en

Alternative title

Kompletne komutativne podalgebre u polinomijalnim puasonovim algebrama: dokaz Mishchenko-Fomenkove hypoteze

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