&LieAlgDB;

A database of Lie algebras

Version 2.1
Serena Cicalò cicalo@science.unitn.it

        	    Dipartimento di Matematica e Informatica

                Via Ospedale, 72

                09124 Cagliari

                Italy

Willem de Graaf degraaf@science.unitn.it http://www.science.unitn.it/~degraaf/

        	   Dipartimento di Matematica

               Via Sommarive, 14

               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

November 2010
This package provides access to the classification of the following families of Lie algebras: non-solvable Lie algebras over finite fields up to dimension 6; nilpotent Lie algebras of dimension up to 9 over GF(2), of dimension up to 7 over GF(3) or GF(5); simple Lie algebras of dimensions between 7 and 9 over GF(2); the classification of solvable Lie algebras of dimension at most 4; the classification of nilpotent Lie algebras of dimensions at most 6.
©right; 2006--2007 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 made. We also acknowledge the effort of the referees to improve the implementation and the documentation.

Serena Cicalò would like to thank the Centro de Álgebra da Universidade de Lisboa for their kind hospitality during July - December 2009 and May - September 2010, when the classification of the 6-dimensional nilpotent Lie algebras over fields of characteristic 2 was made and added to the package.
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 ); nilpotent Lie algebras of dimension up to 9 over GF(2), of dimension up to 7 over GF(3) or GF(5) (from ); simple Lie algebras of dimensions between 7 and 9 over GF(2) (from ); the classification of solvable Lie algebras of dimension at most 4 (from ); the classification of nilpotent Lie algebras of dimension at most 6 (from and ). 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.
<#Include SYSTEM "families.xml">
A description of the Lie algebras that are contained in the package <#Include SYSTEM "appnonsolv.xml"> <#Include SYSTEM "appsimple.xml"> <#Include SYSTEM "appsolv.xml">