Solvable quadratic Lie algebras of dimensions $\leq 8$

TL;DR

This paper classifies solvable quadratic Lie algebras of dimensions up to 8 over algebraically closed fields, using the double extension method to systematically identify all such structures up to isometric isomorphism.

Contribution

It provides a comprehensive classification of low-dimensional solvable quadratic Lie algebras, a task not previously completed for dimensions up to 8.

Findings

Complete classification of solvable quadratic Lie algebras of dimension ≤ 8

Identification of isometric isomorphism classes

Application of the double extension method for classification

Abstract

In this paper, we classify solvable Lie algebras of dimensions $\leq 8$ endowed with a nondegenerate invariant symmetric bilinear form over an algebraically closed field. This classification (up to isometrically isomorphisms) is mainly based on the double extension method.