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arXiv · 1204.1299

Compatible quadratic Poisson brackets related to a family of elliptic curves

Alexander Odesskii·Thomas Wolf
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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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Alexander Odesskii, Thomas Wolf. 2012-05-28. Compatible quadratic Poisson brackets related to a family of elliptic curves. https://doi.org/10.1016/j.geomphys.2012.10.004

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