# On the fibres of Mishchenko-Fomenko systems

@inproceedings{Crooks2019OnTF,
title={On the fibres of Mishchenko-Fomenko systems},
author={Peter A. Crooks and Markus Roser},
year={2019}
}
• Published 2019
This work is concerned with Mishchenko and Fomenko's celebrated theory of completely integrable systems on a complex semisimple Lie algebra $\mathfrak{g}$. Their theory associates a maximal Poisson-commutative subalgebra of $\mathbb{C}[\mathfrak{g}]$ to each regular element $a\in\mathfrak{g}$, and one can assemble free generators of this subalgebra into a moment map $F_a:\mathfrak{g}\rightarrow\mathbb{C}^b$. We examine the structure of fibres in Mishchenko--Fomenko systems, building on the… CONTINUE READING

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