On the algorithm to find S-related Lie algebras

TL;DR

This paper introduces a Java library that automates the S-expansion method for relating Lie algebras using abelian semigroups, including a new fillTemplate method to determine algebra relations.

Contribution

The paper presents a novel Java library for automating the S-expansion process and introduces the fillTemplate method for identifying S-related Lie algebras.

Findings

Library effectively automates S-expansion calculations

fillTemplate method accurately determines algebra relations

Utilizes classified semigroups up to order 6 as input

Abstract

In this article we describe the Java library that we have recently constructed to automatize the S-expansion method, a powerful mathematical technique allowing to relate different Lie algebras. An important input in this procedure is the use of abelian semigroups and thus, we start with a brief review about the classification of non-isomorphic semigroups made in the literature during the last decades, and explain how the lists of non-isomorphic semigroups up to order 6 can be used as inputs in many of the methods of our library. After describing the main features of the classes that compose our library we present a new method called fillTemplate which tuns out to be very useful to answer whether two given algebras can be S-related.