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# LieAlgDB

## A database of Lie algebras

Version 2.0.2

September 2007

Willem de Graaf
Email: degraaf@science.unitn.it
Homepage: http://www.science.unitn.it/~degraaf/
Address:
Dipartimento di Matematica
Via Sommarive 14
I-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 5 and those of dimension 6 over fields of odd characteristic.

### 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 completed. We also acknowledge the effort of the referees to improve the implementation and the documentation.

### 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 NumberOfNilpotentLieAlgebras
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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