Poisson structures on the center of the elliptic algebra A_{p,q}(sl(2)_c)

J. Avan , L. Frappat , M. Rossi , P. Sorba

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classification q-alg hep-thmath.QA

keywords centeralgebraellipticpoissonstructuresalgebrasconstructedcritical

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It is shown that the elliptic algebra A_{p,q}(sl(2)_c) has a non trivial center at the critical level $c=-2$, generalizing the result of Reshetikhin and Semenov-Tian-Shansky for trigonometric algebras. A family of Poisson structures indexed by a non-negative integer $k$ is constructed on this center.

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Poisson structures on the center of the elliptic algebra A_{p,q}(sl(2)_c)

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