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Title: Complete commutative subalgebras in polynomial poisson algebras: a proof of the Mischenko-Fomenko conjecture
Other Titles: Kompletne komutativne podalgebre u polinomijalnim puasonovim algebrama: dokaz Mishchenko-Fomenkove hypoteze
Authors: Bolsinov, Alexey V.
Issue Date: 2016
Publisher: Serbian Society of 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.
Abstract: 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.
Description: 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.
Version: Accepted for publication
DOI: 10.2298/TAM161111012B
URI: https://dspace.lboro.ac.uk/2134/23653
Publisher Link: http://dx.doi.org/10.2298/TAM161111012B
ISSN: 1450-5584
Appears in Collections:Published Articles (Maths)

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