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FinLie

Computation with finite Lie algebras

Version 1.1

01 March 2018

Bettina Eick
Email: beick@tu-bs.de
Homepage: http://www.icm.tu-bs.de/~beick/

Tobias Moede
Email: t.moede@tu-bs.de
Homepage: http://www.icm.tu-bs.de/~tobmoede/

Copyright

FinLie package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

1 Introduction

1.1 Tables

1.1-1 LieTableByBasis
1.1-2 LieAlgebraByTable

1.2 Constructions

  1.2-1 AbelianLieAlgebra
  1.2-2 UnipotentLieAlgebra
  1.2-3 TriangularLieAlgebra
  1.2-4 LieAlgebraTensor
  1.2-5 DerivationsLieAlgebra

2 Cohomology

2.1 First cohomology

2.1-1 LieOneCohomology

2.2 Second cohomology

2.2-1 LieTwoCohomology

2.3 Extensions by cocycles

2.3-1 LieExtensionByCocycle

3 Automorphism groups and isomorphism testing

3.1 Calculation of automorphism groups

3.1-1 AutomorphismGroupOfLieAlgebra

3.2 Isomorphism testing

3.2-1 CanonicalFormOfSolvableLieAlgebra
3.2-2 AreIsomorphicLieAlgebras

4 Simple Lie algebras

4.1 Simple Lie algebras and ideals

  4.1-1 IsSimpleLieAlgebra
  4.1-2 IdealsOfLieAlgebra
  4.1-3 SimpleFactorsLieAlgebra

4.2 Small-dimensional simple Lie algebras over GF(2)

4.2-1 LieAlgebraByLibrary

4.3 Infinite families of simple Lie algebras over GF(2)

  4.3-1 SimpleLieAlgebraByGramMatrix1
  4.3-2 SimpleLieAlgebraByGramMatrix2
  4.3-3 SimpleLieAlgebraAlternateMats
  4.3-4 SimpleLieAlgebraByQuadraticForm

References

Index

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