LieAlgDB
  
  
                           A database of Lie algebras
  
  
                                 Version 2.0.2
  
  
                                 September 2007
  
  
                                Willem de Graaf
  
                                Csaba Schneider
  
  
  
  Willem de Graaf
      Email:    mailto: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:    mailto:csaba.schneider@sztaki.hu
      Homepage: http://www.sztaki.hu/~schneider
      Address:  Informatics Research Laboratory
                Computer and Automation Research Institute
                1518 Budapest Pf. 63.
                Hungary
  
  
  
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  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.
  
  
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  Copyright
  © 2006--2007 Willem de Graaf and Csaba Schneider
  
  
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  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.
  
  
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  Contents (LieAlgDB)
  
  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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