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arXiv · 1406.3777

Generalized argument shift method and complete commutative subalgebras in polynomial Poisson algebras

Anton Izosimov
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Abstract

The Mischenko-Fomenko argument shift method allows to construct commutative subalgebras in the symmetric algebra $S(\mathfrak g)$ of a finite-dimensional Lie algebra $\mathfrak g$. For a wide class of Lie algebras, these commutative subalgebras appear to be complete, i.e. they have maximal transcendence degree. However, for many algebras, Mischenko-Fomenko subalgebras are incomplete or even empty. In this case, we suggest a natural way how to extend Mischenko-Fomenko subalgebras, and give a completeness criterion for these extended subalgebras.

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BibTeXRIS

Anton Izosimov. 2014-06-14. Generalized argument shift method and complete commutative subalgebras in polynomial Poisson algebras. https://arxiv.org/abs/1406.3777

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