# Poisson-commutative subalgebras of $S(\mathfrak g)$ associated with involutions.

@article{Panyushev2018PoissoncommutativeSO, title={Poisson-commutative subalgebras of \$S(\mathfrak g)\$ associated with involutions.}, author={Dmitri I. Panyushev and Oksana Yakimova}, journal={arXiv: Representation Theory}, year={2018} }

The symmetric algebra $S(\mathfrak g)$ of a reductive Lie algebra $\mathfrak g$ is equipped with the standard Poisson structure, i.e., the Lie-Poisson bracket. Poisson-commutative subalgebras of $S(\mathfrak g)$ attract a great deal of attention, because of their relationship to integrable systems and, more recently, to geometric representation theory. The transcendence degree of a Poisson-commutative subalgebra ${\mathcal C}\subset S(\mathfrak g)$ is bounded by the "magic number" $\boldsymbol…

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