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

We give a non-trivial Lie algebra map from the negative cyclic cohomology of an associative algebra with trace, to the space of functions on its Maurer-Cartan solutions. This is a generalized algebraic version of a theorem in \cite{AZ} extending Goldman's result to the equivariant homology of the free loop space.

Mots clés: 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. 2008. ⟨hal-00296647v2⟩