  
  
                                     [1XCoReLG[101X
  
  
                        [1XComputing with real Lie Algebras[101X
  
  
                                  Version 1.20
  
  
                                 December 2014
  
  
                                 Heiko Dietrich
  
                                  Paolo Faccin
  
                                Willem de Graaf
  
  
  
  Heiko Dietrich
      Email:    [7Xmailto:heiko.dietrich@monash.edu[107X
      Homepage: [7Xhttp://users.monash.edu.au/~heikod/[107X
      Address:  [33X[0;14YSchool of Mathematical Sciences[133X
                [33X[0;14YMonash University[133X
                [33X[0;14YWellington Road 1[133X
                [33X[0;14YVIC 3800, Melbourne, Australia[133X
  
  
  Paolo Faccin
      Email:    [7Xmailto:paolofaccin86@gmail.com[107X
      Address:  [33X[0;14YDipartimento di Matematica[133X
                [33X[0;14YVia Sommarive 14[133X
                [33X[0;14YI-38050 Povo (Trento), Italy[133X
  
  
  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), Italy[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThis  package  provides  functions for computing with various aspects of the
  theory of real simple Lie algebras.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2014 Heiko Dietrich, Paolo Faccin, and Willem de Graaf[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThe  research leading to this package has received funding from the European
  Union's  Seventh  Framework  Program  FP7/2007-2013 under grant agreement no
  271712.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (CoReLG)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YThe simple real Lie algebras[133X
    1.2 [33X[0;0YCartan subalgebras and more[133X
    1.3 [33X[0;0YNilpotent orbits[133X
    1.4 [33X[0;0YOn base fields[133X
  2 [33X[0;0YThe field [3XSqrtField[103X[133X
    2.1 [33X[0;0YDefinition of the field[133X
      2.1-1 SqrtFieldIsGaussRat
    2.2 [33X[0;0YConstruction of elements[133X
      2.2-1 Sqroot
      2.2-2 CoefficientsOfSqrtFieldElt
      2.2-3 SqrtFieldEltByCoefficients
      2.2-4 SqrtFieldEltToCyclotomic
      2.2-5 SqrtFieldEltByCyclotomic
    2.3 [33X[0;0YBasic operations[133X
      2.3-1 SqrtFieldMakeRational
      2.3-2 SqrtFieldPolynomialToRationalPolynomial
      2.3-3 SqrtFieldRationalPolynomialToSqrtFieldPolynomial
      2.3-4 Factors
  3 [33X[0;0YReal Lie Algebras[133X
    3.1 [33X[0;0YConstruction of simple real Lie algebras[133X
      3.1-1 RealFormsInformation
      3.1-2 NumberRealForms
      3.1-3 RealFormById
      3.1-4 AllRealForms
      3.1-5 RealFormParameters
      3.1-6 IsRealFormOfInnerType
      3.1-7 IsRealification
      3.1-8 CartanDecomposition
      3.1-9 RealStructure
    3.2 [33X[0;0YIsomorphisms[133X
      3.2-1 IsomorphismOfRealSemisimpleLieAlgebras
    3.3 [33X[0;0YCartan subalgebras and root systems[133X
      3.3-1 MaximallyCompactCartanSubalgebra
      3.3-2 MaximallyNonCompactCartanSubalgebra
      3.3-3 CompactDimensionOfCartanSubalgebra
      3.3-4 CartanSubalgebrasOfRealForm
      3.3-5 CartanSubspace
      3.3-6 RootsystemOfCartanSubalgebra
      3.3-7 ChevalleyBasis
    3.4 [33X[0;0YDiagrams[133X
      3.4-1 VoganDiagram
      3.4-2 SatakeDiagram
  4 [33X[0;0YReal nilpotent orbits[133X
    4.1 [33X[0;0YNilpotent orbits in real Lie algebras[133X
      4.1-1 NilpotentOrbitsOfRealForm
      4.1-2 RealCayleyTriple
      4.1-3 WeightedDynkinDiagram
    4.2 [33X[0;0YNilpotent orbits in real Theta groups[133X
      4.2-1 RealWeylGroup
      4.2-2 CarrierAlgsForNilpOrbsInZGrading
      4.2-3 CarrierAlgsForNilpOrbsInZmGrading
  
  
  [32X
