On IAn and derivations of free lie algebras.

摘要

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 finitely generated free group are given as well as to (2) comparisons of two intensively studied filtrations on these groups.