On IAn and derivations of free Lie algebras

Thesis (Ph. D.)--University of Rochester. Dept. of Mathematics, 2010.This thesis gives a new, additional structure for the Lie algebra of derivations of free Lie algebras. The new structure arises from actions of a classical algebra known as the Schur algebra. The thesis gives additional structure for (i) the Schur algebras, (ii) their action on the Lie algebra of derivations of a free Lie algebra, and (iii) the operad structures constructed from the Schur algebras and their subalgebras which act on the Lie algebra of derivations of a free Lie algebra. In addition, the entire Lie algebra of derivations is shown to be generated by quadratic derivations together with the action of the Schur operad. Applications to (1) certain subgroups of the automorphism group of a nitely generated free group are given as well as to (2) comparisons of two intensively studied ltrations on these groups