Journal of Noncommutative Geometry

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Volume 4, Issue 3, 2010, pp. 331–347
DOI: 10.4171/JNCG/58

Published online: 2010-07-26

Algebraic string bracket as a Poisson bracket

Hossein Abbaspour[1], Thomas Tradler[2] and Mahmoud Zeinalian[3]

(1) Université de Nantes, France
(2) New York City College of Technology, USA
(3) 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.

Keywords: Free loop space, cyclic homology, symplectic reduction

Abbaspour Hossein, Tradler Thomas, Zeinalian Mahmoud: Algebraic string bracket as a Poisson bracket. J. Noncommut. Geom. 4 (2010), 331-347. doi: 10.4171/JNCG/58