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# LieAlgDB

## A database of Lie algebras

Version 1.0

October 2006

Willem de Graaf
e-mail: degraaf@science.unitn.it
WWW: http://www.science.unitn.it/~degraaf/
Address:
Dipartimento di Matematica
Via Sommarive 14
I-38050 Povo (Trento)
Italy

Csaba Schneider
e-mail: csaba.schneider@sztaki.hu
WWW: 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 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

(C) 2006 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.

### 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 NonSolvableLieAlgebras
2.1-8 SimpleLieAlgebras
2.2 Solvable and nilpotent Lie algebras
2.2-1 SolvableLieAlgebra
2.2-2 NilpotentLieAlgebra
2.2-3 SolvableLieAlgebras
2.2-4 NilpotentLieAlgebras
2.2-5 NumberOfNilpotentLieAlgebras
2.2-6 LieAlgebraIdentification
A. Description of the solvable and nilpotent Lie algebras
B. Description of the non-solvable Lie algebras
B.1 Dimension 3
B.2 Dimension 4
B.3 Dimension 5
B.3-1 Characteristic 2
B.3-2 Odd characteristic
B.4 Dimension 6
B.4-1 Characteristic 2
B.4-2 General odd characteristic
B.4-3 Characteristic 3
B.4-4 Characteristic 5

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