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

2023/07/19 by И. К. Козлов, Kozlov, I. K.
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2307.10418

openalex publication_date 2023/07/19 · openalex created_date 2023/07/23 · openalex updated_date 2026/07/28

Abstract

We study commutative subalgebras in the symmetric algebra S(\mathfrakg) of a finite-dimensional Lie algebra \mathfrakg. A. M. Izosimov introduced extended Mischenko-Fomenko subalgebras 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 \mathfrakg. We prove that the new commutative subalgebras have the same transcendence degree as F_a.

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