On Schur Algebras and Derivations of Free Lie Algebras

TL;DR

This paper explores the interaction between Schur algebras and derivations of free Lie algebras, revealing how derivations are generated and applying findings to automorphism groups of free groups.

Contribution

It demonstrates that derivations are generated by quadratic derivations and Schur operad actions, providing new insights into algebraic structures and automorphism groups.

Findings

Derivations are generated by quadratic derivations and Schur operad actions.

Established connections between Schur algebra actions and derivations of free Lie algebras.

Applied results to subgroups of automorphism groups of free groups.

Abstract

We investigate the action of Schur algebra on the Lie algebras of derivations of free Lie algebras and operad structures constructed from it. We also show that the Lie algebra of derivations is generated by quadratic derivations together with the action of the Schur operad. Applications to certain subgroups of the automorphism group of a finitely generated free group are given as well.