Abstract
We construct quadratic finite-dimensional Poisson algebras corresponding to a rank-N degree-one vector bundle over an elliptic curve with n marked points and also construct the quantum version of the algebras. The algebras are parameterized by the moduli of curves. For N = 2 and n = 1, they coincide with Sklyanin algebras. We prove that the Poisson structure is compatible with the Lie-Poisson structure defined on the direct sum of n copies of sl(N). The origin of the algebras is related to the Poisson reduction of canonical brackets on an affine space over the bundle cotangent to automorphism groups of vector bundles.
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