  
  
                                      [1XSLA[101X
  
  
                              [1XSimple Lie Algebras[101X
  
  
                                  Version 1.1
  
  
                                  January 2016
  
  
                                Willem de Graaf
  
  
  
  Willem de Graaf
      Email:    [7Xmailto:degraaf@science.unitn.it[107X
      Homepage: [7Xhttp://www.science.unitn.it/~degraaf/[107X
      Address:  [33X[0;14YDipartimento di Matematica[133X
                [33X[0;14YVia Sommarive 14[133X
                [33X[0;14YI-38050 Povo (Trento)[133X
                [33X[0;14YItaly[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThis  package  provides  functions for computing with various aspects of the
  theory of simple Lie algebras in characteristic zero.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2016 Willem de Graaf[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (SLA)[101X
  
  1 [33X[0;0YIntroduction[133X
  2 [33X[0;0YAuxiliary Functions[133X
    2.1 [33X[0;0YRoot Systems[133X
      2.1-1 ExtendedCartanMatrix
      2.1-2 CartanType
      2.1-3 WeylTransversal
      2.1-4 SizeOfWeylGroup
    2.2 [33X[0;0YLie Algebras and Their Modules[133X
      2.2-1 IsomorphismOfSemisimpleLieAlgebras
      2.2-2 AdmissibleLattice
      2.2-3 DirectSumDecomposition
      2.2-4 CharacteristicsOfStrata
  3 [33X[0;0YNilpotent Orbits[133X
    3.1 [33X[0;0YThe functions[133X
      3.1-1 NilpotentOrbit
      3.1-2 NilpotentOrbits
      3.1-3 WeightedDynkinDiagram
      3.1-4 WeightedDynkinDiagram
      3.1-5 AmbientLieAlgebra
      3.1-6 SemiSimpleType
      3.1-7 SL2Triple
      3.1-8 RandomSL2Triple
      3.1-9 SL2Grading
      3.1-10 SL2Triple
      3.1-11 InducedNilpotentOrbits
      3.1-12 RigidNilpotentOrbits
  4 [33X[0;0YFinite Order Automorphisms and [22Xθ[122X-Groups[133X
    4.1 [33X[0;0YThe functions[133X
      4.1-1 FiniteOrderInnerAutomorphisms
      4.1-2 FiniteOrderOuterAutomorphisms
      4.1-3 Order
      4.1-4 KacDiagram
      4.1-5 Grading
      4.1-6 NilpotentOrbitsOfThetaRepresentation
      4.1-7 ClosureDiagram
      4.1-8 CarrierAlgebra
      4.1-9 CartanSubspace
  5 [33X[0;0YSemisimple Subalgebras of Semisimple Lie Algebras[133X
    5.1 [33X[0;0YBranching[133X
      5.1-1 ProjectionMatrix
      5.1-2 Branching
    5.2 [33X[0;0YConstructing Semisimple Subalgebras[133X
      5.2-1 RegularSemisimpleSubalgebras
      5.2-2 SSSTypes
      5.2-3 LieAlgebraAndSubalgebras
      5.2-4 InclusionsGraph
      5.2-5 SubalgebrasInclusion
      5.2-6 DynkinIndex
      5.2-7 AreLinearlyEquivalentSubalgebras
      5.2-8 MakeDatabaseEntry
  
  
  [32X
