Automatic classification of automorphisms of lower-dimensional Lie algebras

TL;DR

This paper introduces two algorithms implemented in MATHEMATICA for classifying automorphisms of lower-dimensional Lie algebras, facilitating symmetry analysis in differential equations.

Contribution

It presents a novel MATHEMATICA package with brute-force and evolutionary algorithms for automorphism classification of Lie algebras, including tools for symmetry analysis.

Findings

Algorithms successfully classify automorphisms of Lie algebras

The package aids in symmetry analysis of differential equations

Examples demonstrate effectiveness of the approach

Abstract

We implement two algorithms in MATHEMATICA for classifying automorphisms of lower-dimensional non-commutative Lie algebras. The first algorithm is a brute-force approach whereas the second is an evolutionary strategy. These algorithms are delivered as the MATHEMATICA package cwsAutoClass. In order to facilitate the application of this package to symmetry Lie algebras of differential equations, we also provide a package, cwsLieSymTools, for manipulating finite-dimensional Lie algebras of vector fields. In particular, this package allows the computations of Lie brackets, structure constants, and the visualization of commutator tables. Several examples are provided to illustrate the pertinence of our approach.