Derivations and automorphisms of free nilpotent Lie algebras and their quotiens

TL;DR

This paper characterizes derivations and automorphisms of free nilpotent Lie algebras and extends these results to generic nilpotent Lie algebras of the same type and nilindex, with illustrative examples.

Contribution

It provides a detailed description of derivations and automorphisms for free nilpotent Lie algebras and applies these findings to broader classes of nilpotent Lie algebras.

Findings

Explicit descriptions of derivation algebras

Explicit descriptions of automorphism groups

Illustrative examples of the theoretical results

Abstract

Let $\n_{d,t}$ be the free nilpotent Lie algebra of type $d$ and nilindex $t$. Starting out with the derivation algebra and the automorphism group of $\n_{d,t}$, we get a natural description of derivations and automorphisms of any generic nilpotent Lie algebra of the same type and nilindex. Moreover, along the paper we discuss several examples to illustrate the obtained results.