2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225836We consider the Lie algebra consisting of all derivations on the free associative algebra, generated by the first homology group of a closed oriented surface, which kill the symplectic class. We find the first non-trivial abelianization of this Lie algebra and discuss its relation to unstable cohomology classes of the moduli space of curves via a theorem of Kontsevich.This is the version published by Geometry & Topology Monographs on 25 February 2008Geometric TopologyAlgebraic Geometry17B40, 17B56, 32G15text