JournalsjncgVol. 4 , No. 3DOI 10.4171/jncg/58

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
Algebraic string bracket as a Poisson bracket cover

Abstract

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.