We 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.
Keywords
derivation, homology of Lie algebras,
moduli space of curves,