An Abelian Quotient of the Symplectic Derivation Lie Algebra of the Free Lie Algebra

Abstract

ABSTRACT. We construct an abelian quotient of the symplectic derivation Lie algebra h g,1 of the free Lie algebra generated by the fundamental representation of Sp(2g, Q). More specifically, we show that the weight 12 part of the abelianization of h g,1 is 1-dimensional for g ≥ 8.The computation is done with the aid of computers.