GAP (LieAlgDB) - Chapter 1: Introduction

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1 Introduction

### 1 Introduction

This is the manual for the GAP package LieAlgDB, for accessing and working with several classifications of Lie algebras.

In the mathematical literature many classifications of Lie algebras of various types have been published (we refer to the bibliography for a few examples). However, working with these classifications from paper is not always easy. This package aims at making a few classifications of small-dimensional Lie algebras that have appeared in recent years more accessible. For each classification that is contained in the package, functions are provided that construct Lie algebras from that classification inside GAP. This allows the user to obtain easy access to the often rather complicated data contained in a classification, and to directly interface the Lie algebras to the functionality for Lie algebras which is already contained in the system.

The package contains the following classifications:

- non-solvable Lie algebras over finite fields up to dimension 6 (from [Str]);

- nilpotent Lie algebras of dimension up to 9 over GF(2), of dimension up to 7 over GF(3) or GF(5) (from [Sch05]);

- simple Lie algebras of dimensions between 7 and 9 over GF(2) (from [VL06]);

- the classification of solvable Lie algebras of dimension at most 4 (from [dG05]);

- the classification of nilpotent Lie algebras of dimension at most 6 (from [dG07] and [CdGS11]).

This manual is structured as follows. The next chapter contains a description of the main functions of the package. The third chapter contains descriptions of the classifications used in the package. Most of these are contained in published papers, but for the convenience of the user they have been added here.

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