Algebraic string bracket as a Poisson bracket

Hossein Abbaspour (1) , Thomas Tradler (2) , Mahmoud Zeinalian (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 College of Technology of the City University of New York
3 Long Island University

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.

Mots clés: Free loop space; Cyclic homology; Maurer Cartan; Symplectic reduction

Domaines: Topologie algébrique [math.AT]; Géométrie algébrique [math.AG]; Topologie géométrique [math.GT]

Hossein Abbaspour, Thomas Tradler, Mahmoud Zeinalian. Algebraic string bracket as a Poisson bracket. Journal of Noncommutative Geometry, 2010, 2. ⟨hal-00296647v3⟩