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# LieAlgDB

## A database of Lie algebras

Version 2.1

November 2010

Serena Cicalò
Email: cicalo@science.unitn.it
Address:
Dipartimento di Matematica e Informatica
Via Ospedale, 72
09124 Cagliari
Italy

Willem de Graaf
Email: degraaf@science.unitn.it
Homepage: http://www.science.unitn.it/~degraaf/
Address:
Dipartimento di Matematica
Via Sommarive, 14
38050 Povo (Trento)
Italy

Csaba Schneider
Email: csaba.schneider@sztaki.hu
Homepage: http://www.sztaki.hu/~schneider
Address:
Informatics Research Laboratory
Computer and Automation Research Institute
1518 Budapest Pf. 63.
Hungary

### Abstract

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.

### Copyright

© 2006--2007 Willem de Graaf and Csaba Schneider

### Acknowledgements

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.

### Contents

1 Introduction
2 The families of Lie algebras included in the database
2.1 Non-solvable Lie algebras
2.1-1 NonSolvableLieAlgebra
2.1-2 Dimension 1 and 2
2.1-3 Dimension 3
2.1-4 Dimension 4
2.1-5 Dimension 5
2.1-6 Dimension 6
2.1-7 AllNonSolvableLieAlgebras
2.1-8 AllSimpleLieAlgebras
2.2 Solvable and nilpotent Lie algebras
2.2-1 SolvableLieAlgebra
2.2-2 NilpotentLieAlgebra
2.2-3 AllSolvableLieAlgebras
2.2-4 AllNilpotentLieAlgebras
2.2-5 NrNilpotentLieAlgebras
2.2-6 LieAlgebraIdentification
3 A description of the Lie algebras that are contained in the package
3.1 Description of the non-solvable Lie algebras
3.2 Dimension 3
3.3 Dimension 4
3.4 Dimension 5
3.4-1 Characteristic 2
3.4-2 Odd characteristic
3.5 Dimension 6
3.5-1 Characteristic 2
3.5-2 General odd characteristic
3.5-3 Characteristic 3
3.5-4 Characteristic 5
3.6 Description of the simple Lie algebras
3.7 Description of the solvable and nilpotent Lie algebras
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