  In this paper we construct a Lie algebra representation of the algebraic
string bracket on negative cyclic cohomology of an associative algebra with
appropriate duality. This is a generalized algebraic version of the main
theorem of [AZ] which extends Goldman's results using string topology
operations.The main result can be applied to the de Rham complex of a smooth
manifold as well as the Dolbeault resolution of the endomorphisms of a
holomorphic bundle on a Calabi-Yau manifold.
