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Magma
Computer • algebra
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Introduction
Generalized Cartan Matrices
IsGeneralizedCartanMatrix(C) : AlgMatElt -> BoolElt
KacMoodyClass(C) : AlgMatElt -> MonStgElt, ModMatRngElt
KacMoodyClasses(C) : AlgMatElt -> SeqEnum, SeqEnum, SeqEnum
Example
AlgLieKM_generalized-cartan (H108E1)
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 (H108E2)
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 (H108E3)
Constructing Elements of Affine Kac-Moody Lie Algebras
L . i : AlgKac, RngIntElt -> AlgKacElt
HasAttribute(L, "c") : AlgKac, MonStgElt -> BoolElt, AlgKacElt
elt<L | < [ (<) p
1
, y
1
(>), ... ], 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 (H108E4)
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V2.28, 28 February 2025