Relations between Derivations arising from Modular Forms

Abstract

Denote by L(a; b) the free complex Lie algebra on the two generators a and b. For each integer m 0 there is a derivation 2m on L(a; b) that satis es 2m([a; b]) = 0 and 2m(a) = ad(a)2m(b). In this paper we study the derivation subalgebra u generated by the 2m. In particular, we study the relations between the 2m and nd that these relations are related to the period polynomials of modular forms.