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Using the ideas of string topology of Chas-Sullivan, we define a linear map $\\{\\{-,-\\}\\}: A \\otimes A \\to A\\otimes A$ which is a double bracket in the sense of Van den Bergh satisfying a version of the Jacobi identity. For $\\dim(M)\\geq 3$, the double bracket $\\{\\{-,-\\}\\}$ induces Gerstenhaber brackets in the representation algebras associated with $A$. 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