  
  
                                     [1X[5XSophus[105X[101X
  
  
                      [1XComputing in nilpotent Lie algebras[101X
  
  
                                  Version 1.23
  
  
                                 February 2006
  
  
                                Csaba Schneider
  
  
  
  Csaba Schneider
      Email:    [7Xmailto:csaba.schneider@sztaki.hu[107X
      Homepage: [7Xhttp://www.sztaki.hu/~schneider[107X
      Address:  [33X[0;14YInformatics Laboratory[133X
                [33X[0;14YComputer and Automation Research Institute[133X
                [33X[0;14YThe Hungarian Academy of Sciences[133X
                [33X[0;14Y1111 Budapest, L\'agym\'anyosi u.\ 11.[133X
                [33X[0;14YHungary[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0Y[5XSophus[105X is a GAP~4 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
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YMost  of  the  work  on this package was carried out while I held a research
  position  at  the  Technische  Universtit\"at  Braunschweig. I would like to
  express  my  gratitude  to  the staff and the students of the Institut f\"ur
  Geometrie for their interest in this work. Special thanks go to Bettina Eick
  for her r\^ole 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 ReadStringToNilpotentLieAlgebra
      3.7-3 WriteLieAlgebraListToFile
      3.7-4 SophusBuildManual
      3.7-5 SophusBuildManualHTML
  
  
  [32X
