Centralizers of certain quadratic elements in Poisson--Lie algebras and Argument Shift method

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dc.creatorRybnikov, Leonid
dc.date2006-08-23
dc.date2006-11-08
dc.date.accessioned2026-07-07T07:22:05Z
dc.date.available2026-07-07T07:22:05Z
dc.descriptionWe study maximal Poisson-commutative subalgebras in the Poisson algebra $S(\mathfrak{g})$ of a semisimple Lie algebra $\mathfrak{g}$ constructed by Mischenko and Fomenko with the help of the argument shift method. We prove that these subalgebras are Poisson centralizers of certain quadratic elements of $S(\mathfrak{g})$. We deduce from this that there is a unique quantization of Mischenko--Fomenko subalgebras, i.e. there is a unique way to lift Mischenko--Fomenko subalgebras to commutative subalgebras of the universal enveloping algebra $U(\mathfrak{g})$.
dc.description4 pages, references added
dc.identifierhttps://arxiv.org/abs/math/0608586
dc.identifierhttp://arxiv.org/abs/math/0608586
dc.identifierUMN 60 (2005), No 2, pp.173--174 (Russian)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115534
dc.subjectQuantum Algebra
dc.titleCentralizers of certain quadratic elements in Poisson--Lie algebras and Argument Shift method
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