Introduction

 
Generalized Cartan Matrices
      IsGeneralizedCartanMatrix(C) : AlgMatElt -> BoolElt
      KacMoodyClass(C) : AlgMatElt -> MonStgElt, ModMatRngElt
      KacMoodyClasses(C) : AlgMatElt -> SeqEnum, SeqEnum, SeqEnum
      Example AlgLieKM_generalized-cartan (H111E1)

 
Affine Kac--Moody Lie Algebras

      Constructing Affine Kac--Moody Lie Algebras
            AffineLieAlgebra(N, F) : MonStgElt, Fld -> AlgKac
            AffineLieAlgebra(C, F) : AlgMatElt, Fld -> AlgKac
            Example AlgLieKM_construct (H111E2)

      Properties of Affine Kac--Moody Lie Algebras
            CartanMatrix(L) : AlgKac -> AlgMatElt
            CartanName(L) : AlgKac -> MonStgElt
            Dimension(L) : AlgKac -> Infty
            CoefficientRing(L) : AlgKac -> Rng
            FiniteLieAlgebra(L) : AlgKac -> AlgLie
            LaurentSeriesRing(L) : AlgKac -> RngSerLaur
            StandardGenerators(L) : AlgKac -> SeqEnum[AlgKacElt], SeqEnum[AlgKacElt], SeqEnum[AlgKacElt]
            Example AlgLieKM_construct (H111E3)

      Constructing Elements of Affine Kac--Moody Lie Algebras
            L . i : AlgKac, RngIntElt -> AlgKacElt
            HasAttribute(L, "c") : AlgKac, MonStgElt -> BoolElt, AlgKacElt
            elt<L | < [ (<) p₁, y₁ (>), ... ], λ, μ (>) > : AlgKac, Tup -> AlgKacElt

      Properties of Elements of Affine Kac--Moody Lie Algebras
            EltTup(x) : AlgKacElt -> Tup
            IsZero(x) : AlgKacElt -> BoolElt
            x eq y : AlgKacElt, AlgKacElt -> BoolElt
            x + y : AlgKacElt, AlgKacElt -> AlgKacElt
            -x : AlgKacElt -> AlgKacElt
            Example AlgLieKM_construct (H111E4)

 
Bibliography

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