Classification of quadratic Lie algebras of low dimension

TL;DR

This paper classifies low-dimensional irreducible non-solvable quadratic Lie algebras, providing a comprehensive list of such structures with invariant bilinear forms.

Contribution

It offers the first complete classification of irreducible non-solvable quadratic Lie algebras up to dimension 13.

Findings

Complete list of classified Lie algebras up to dimension 13

Identification of invariant bilinear forms in these algebras

Clarification of structure for non-solvable cases

Abstract

In this paper we give the classification of the irreducible non solvable Lie algebras of dimensions $\leq 13$ with nondegenerate, symmetric and invariant bilinear forms.