Compatible quadratic Poisson brackets related to a family of elliptic curves

Published 5 Apr 2012 in math.QA, math.AG, and nlin.SI | (1204.1299v2)

Abstract: We construct nine pairwise compatible quadratic Poisson structures such that a generic linear combination of them is associated with an elliptic algebra in n generators. Explicit formulas for Casimir elements of this elliptic Poisson structure are obtained.

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