Inner and Outer Automorphisms of Free Metabelian Nilpotent Lie algebras

TL;DR

This paper characterizes the groups of automorphisms of free metabelian nilpotent Lie algebras over fields of characteristic zero, including their completions, providing a detailed structural understanding.

Contribution

It provides a comprehensive description of inner and outer automorphism groups for these Lie algebras and their completions, advancing the algebraic theory of automorphisms.

Findings

Inner and outer automorphism groups are explicitly described.

Automorphisms of the completed algebra are characterized.

Structural insights into automorphisms of free metabelian nilpotent Lie algebras.

Abstract

We describe the groups of inner and outer automorphisms of the free metabelian nilpotent Lie algebra of finite rank over a field of characteristic 0. To obtain this result we first describe the groups of inner and continuous outer automorphisms of the completion with respect to the formal power series topology of the free metabelian Lie algebra finite rank.