ADDENDUM TO "AN ABELIAN QUOTIENT OF THE SYMPLECTIC DERIVATION LIE ALGEBRA OF THE FREE LIE ALGEBRA" (Topology and Analysis of Discrete Groups and Hyperbolic Spaces)

Abstract

In our previous paper, we gave an explicit description of an abelian quotient of the symplectic derivation Lie algebra mathfrak{h}_{g, 1} of the free Lie algebra generated by the fundamental representation of mathrm{S}mathrm{p}(2g, mathbb{Q}). This abelian quotient is 1-dimensional and lives in weight 12 part. Here we show that the corresponding quotient map C : mathfrak{h}_{g, 1}(12) rightarrow mathbb{Q} factors through the Enomoto-Satoh map ES_{12} of degree 12.