Abstract
For the direct sum of several copies of sln, a family of Lie brackets compatible with the initial one is constructed. The structure constants of these brackets are expressed in terms of θ functions associated with an elliptic curve. The structure of Casimir elements for these brackets is investigated. A generalization of this construction to the case of vector-valued θ-functions is presented. A different procedure for constructing compatible Lie brackets based on the argument shift method for quadratic Poisson brackets is discussed.
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