## &LieAlgDB;

A database of Lie algebras
Version 1.0
Willem de Graaf degraaf@science.unitn.it http://www.science.unitn.it/~degraaf/

        	    Dipartimento di Matematica

    Via Sommarive 14

    I-38050 Povo (Trento)

    Italy

Csaba Schneider csaba.schneider@sztaki.hu http://www.sztaki.hu/~schneider

        	    Informatics Research Laboratory

        	    Computer and Automation Research Institute

        	    1518 Budapest Pf. 63.

        	    Hungary

October 2006

This package provides access to the the classification of the following families of Lie algebras: solvable Lie algebras of dimension at most 4; nilpotent Lie algebras of dimension at most 5, and those of dimension~6 over a field of characteristic different from 2; non-solvable Lie algebras of dimension at most 6 over finite fields; simple Lie algebras of dimension at most 6 over finite fields and those of dimension at most 9 over GF(2).

&copyright; 2006 Willem de Graaf and Csaba Schneider
We are grateful to Andrea Caranti, Marco Costantini, Bettina Eick, Helmut Strade, Michael Vaughan-Lee. Without their help, interest, and encouragement, this package would not have been completed.
Introduction

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

In the mathematics 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 &GAP;.

The package contains the following classifications: non-solvable Lie algebras over finite fields up to dimension 6 (from ), nilpotent Lie algebras of dimension upto 9 over F=GF(2), of dimension upto 7 over F=GF(3) or F=GF(5) (from ), simple Lie algebras of dimensions between 7 and 9 over F=GF(2) (from ), the classification of solvable Lie algebras of dimensions 2,3, and 4 (from ), the classification of nilpotent Lie algebras of dimensions 5 and 6 (from ).

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

<#Include SYSTEM "families.xml">

<#Include SYSTEM "appsolv.xml"> <#Include SYSTEM "appnonsolv.xml">