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 to the Dolbeault resolution of the endomorphisms of a holomorphic bundle on a Calabi–Yau manifold.
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Hossein Abbaspour, Thomas Tradler, Mahmoud Zeinalian, Algebraic string bracket as a Poisson bracket. J. Noncommut. Geom. 4 (2010), no. 3, pp. 331–347DOI 10.4171/JNCG/58