Automorphism group and ad-invariant metric on all six dimensional solvable real Lie algebras

TL;DR

This paper computes the automorphism groups and ad-invariant metrics for all six-dimensional solvable real Lie algebras with nilradicals of dimensions 3, 4, and 5, using the adjoint representation.

Contribution

It provides a comprehensive calculation of automorphism groups and ad-invariant metrics for all relevant six-dimensional solvable real Lie algebras, filling a gap in the classification.

Findings

Automorphism groups explicitly determined for each algebra.

Ad-invariant metrics identified for all cases.

Enhanced understanding of structure and symmetries of these Lie algebras.

Abstract

Using adjoint representation of Lie algebras, we calculate the automorphism group and ad-invariant metric on six dimensional solvable real Lie algebras with 5, 4 and 3 dimensional nilradicals.