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The paper is devoted to the Poisson brackets compatible with multiplicationin associative algebras. These brackets are shown to be quadratic and theirrelations with the classical Yang--Baxter equation are revealed. The paper alsocontains a description of Poisson Lie structures on Lie groups whose Liealgebras are adjacent to an associative structure.Comment: 16 pages, latex, no figure

Quadratic Poisson brackets and the Drinfeld theory for associative algebras