Algebraic string bracket as a Poisson bracket

  • Hossein Abbaspour

    Université de Nantes, France
  • Thomas Tradler

    New York City College of Technology, USA
  • Mahmoud Zeinalian

    Long Island University, Brookville, NY, USA


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.

Cite this article

Hossein Abbaspour, Thomas Tradler, Mahmoud Zeinalian, Algebraic string bracket as a Poisson bracket. J. Noncommut. Geom. 4 (2010), no. 3, pp. 331–347

DOI 10.4171/JNCG/58