Polynomilal Poisson algebras with regular structure of symplectic leaves

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dc.creatorOdesskii, A.
dc.creatorRubtsov, V.
dc.date2001-10-02
dc.date.accessioned2026-07-07T04:43:38Z
dc.date.available2026-07-07T04:43:38Z
dc.descriptionWe study polynomial Poisson algebras with some regularity conditions. Linear (Lie-Berezin-Kirillov) structures on dual spaces of semi-simple Lie algebras, quadratic Sklyanin elliptic algebras of \cite{FO1},\cite{FO2} as well as polynomial algebras recently described by Bondal-Dubrovin-Ugaglia (\cite{Bondal},\cite{Ug}) belong to this class. We establish some simple determinantal relations between the brackets and Casimirs in this algebras. These relations imply in particular that for Sklyanin elliptic algebras the sum of Casimir degrees coincides with the dimension of the algebra. We are discussing some interesting examples of these algebras and in particular we show that some of them arise naturally in Hamiltonian integrable systems. Among these examples is a new class of two-body integrable systems admitting an elliptic dependence both on coordinates and momenta.
dc.description21 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0110032
dc.identifierhttp://arxiv.org/abs/math/0110032
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62306
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.subject17B63
dc.titlePolynomilal Poisson algebras with regular structure of symplectic leaves
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