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arXiv · 1206.3882

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

Alexey Bolsinov
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Abstract

The Mishchenko-Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra $\goth g$ there exists a complete set of commuting polynomials on its dual space $\goth g^*$. In terms of the theory of integrable Hamiltonian systems this means that the dual space $\goth g^*$ endowed with the standard Lie-Poisson bracket admits polynomial integrable Hamiltonian systems. Recently this conjecture has been proved by S.T. Sadetov. Following his idea, we give an explicit geometric construction for commuting polynomials on $\goth g^*$ and consider some examples.

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Alexey Bolsinov. 2012-06-18. Complete commutative subalgebras in polynomial Poisson algebras: a proof of the Mischenko--Fomenko conjecture. https://arxiv.org/abs/1206.3882

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