  
  
                                    [1X Sophus [101X
  
  
                     [1X Computing in nilpotent Lie algebras [101X
  
  
                                      1.27
  
  
                                 9 August 2022
  
  
                                Csaba Schneider
  
  
  
  Csaba Schneider
      Email:    [7Xmailto:csaba@mat.ufmg.br[107X
      Homepage: [7Xhttp://www.mat.ufmg.br/~csaba/[107X
      Address:  [33X[0;14YDepartamento de Matemática[133X
                [33X[0;14YInstituto de Ciências Exatas[133X
                [33X[0;14YUniversidade Federal de Minas Gerais (UFMG)[133X
                [33X[0;14YBelo Horizonte, Brasil[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0Y[5XSophus[105X  is a GAP4 package to compute with nilpotent Lie algebras over finite
  prime  fields.  In  particular,  the  package can be used to compute certain
  central  extensions  and the automorphism group of such Lie algebras. [5XSophus[105X
  also  enables  its  user  to  test  isomorphism  between  two  nilpotent Lie
  algebras. The author of the package used it to construct all Lie algebras of
  dimension at most 9 over [23X\mathbb F_2[123X.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2004, 2005 Csaba Schneider[133X
  
  [33X[0;0YThe  [5XSophus[105X  package is free software; you can redistribute it and/or modify
  it    under    the    terms    of    the    GNU   General   Public   License
  ([7Xhttp://www.fsf.org/licenses/gpl.html[107X)  as  published  by  the Free Software
  Foundation;  either  version 2 of the License, or (at your option) any later
  version.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YMost  of  the  work  on this package was carried out while I held a research
  position at the Technische Universität Braunschweig. I would like to express
  my gratitude to the staff and the students of the Institut für Geometrie for
  their  interest in this work. Special thanks go to Bettina Eick for her rôle
  in completing this project.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (Sophus)[101X
  
  1 [33X[0;0YThe theory[133X
  2 [33X[0;0YA sample calculation with [5XSophus[105X[133X
  3 [33X[0;0Y[5XSophus[105X functions[133X
    3.1 [33X[0;0YSome general functions to compute with Lie algebras[133X
      3.1-1 SophusTest
      3.1-2 IsLieNilpotentOverFp
      3.1-3 MinimalGeneratorNumber
      3.1-4 AbelianLieAlgebra
    3.2 [33X[0;0YFunctions to compute with nilpotent bases[133X
      3.2-1 NilpotentBasis
      3.2-2 LieNBWeights
      3.2-3 LieNBDefinitions
      3.2-4 IsNilpotentBasis
      3.2-5 IsLieAlgebraWithNB
    3.3 [33X[0;0YThe cover[133X
      3.3-1 LieCover
      3.3-2 CoverHomomorphism
      3.3-3 CoverOf
      3.3-4 IsLieCover
      3.3-5 LieMultiplicator
      3.3-6 LieNucleus
    3.4 [33X[0;0YAutomorphisms of nilpotent Lie algebras[133X
      3.4-1 NilpotentLieAutomorphism
      3.4-2 IdentityNilpotentLieAutomorphism
      3.4-3 IsNilpotentLieAutomorphism
    3.5 [33X[0;0YAutomorphism group and isomorphism testing[133X
      3.5-1 AutomorphismGroup
      3.5-2 AutomorphismGroupNilpotentLieAlgebra
      3.5-3 AreIsomorphicNilpotentLieAlgebras
    3.6 [33X[0;0YDescendants[133X
      3.6-1 Descendants
      3.6-2 DescendantsOfStep1OfAbelianLieAlgebra
    3.7 [33X[0;0YInput and output[133X
      3.7-1 WriteLieAlgebraToString
      3.7-2 ReadStringToNilpotentLieAlgebraOverFp
      3.7-3 WriteLieAlgebraListToFile
  
  
  [32X
