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arXiv · 2307.10418

Shifts of semi-invariants and complete commutative subalgebras in polynomial Poisson algebras

I. K. Kozlov
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Abstract

We study commutative subalgebras in the symmetric algebra $S(\mathfrak{g})$ of a finite-dimensional Lie algebra $\mathfrak{g}$. A. M. Izosimov introduced extended Mischenko-Fomenko subalgebras $\tilde{\mathcal{F}}_a$ and gave a completeness criterion for them. We generalize his construction and extend Mischenko-Fomenko subalgebras with the shifts of all semi-invariants of $\mathfrak{g}$. We prove that the new commutative subalgebras have the same transcendence degree as $\tilde{\mathcal{F}}_a$.

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BibTeXRIS

I. K. Kozlov. 2023-07-19. Shifts of semi-invariants and complete commutative subalgebras in polynomial Poisson algebras. https://arxiv.org/abs/2307.10418

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