Construction of a Lie Structure Constant Algebra
LieAlgebra< R, n | Q : parameters > : Rng, RngIntElt, SeqEnum -> AlgLie
LieAlgebra< R, n | T : parameters > : Rng, RngIntElt, SeqEnum -> AlgLie
LieAlgebra(A) : AlgAss -> AlgLie
Construction of Simple Lie Algebras
SimpleLieAlgebra(X, n, F) : MonStgElt, RngIntElt, Fld -> AlgLie
Example AlgLie_SimpleLieAlgebra (H75E1)
Root Systems
RootSystem(L) : AlgLie -> [ AlgLieElt ], [ AlgLieElt ], [ AlgLieElt ], [[]]
Example AlgLie_RootSystem (H75E2)
Operations on Lie Algebras
Centre(L) : AlgLie -> AlgLie
Centralizer(L, K) : AlgLie, AlgLie -> AlgLie
Normalizer(L, K) : AlgLie, AlgLie -> AlgLie
SolvableRadical(L) : AlgLie -> AlgLie
NilRadical(L) : AlgLie -> AlgLie
Example AlgLie_Operations (H75E3)
Cartan Subalgebra
CartanSubalgebra(L) : AlgLie -> AlgLie
Example AlgLie_CartanSubalgebra (H75E4)
Series
DerivedSeries(L) : AlgLie -> [ AlgLie ]
LowerCentralSeries(L) : AlgLie -> [ AlgLie ]
UpperCentralSeries(L) : AlgLie -> [ AlgLie ]
Example AlgLie_Series (H75E5)
Decomposition
DirectSumDecomposition(L) : AlgLie -> [ AlgLie ]
Example AlgLie_DirectSumDecomposition (H75E6)
Predicates
IsSolvable(L) : AlgLie -> BoolElt
IsNilpotent(L) : AlgLie -> BoolElt
IsRestrictedLieAlgebra(L) : AlgLie -> BoolElt
HasLeviSubalgebra(L) : AlgLie -> BoolElt
Example AlgLie_Predicates (H75E7)
The Type of a Semisimple Lie Algebra
SemiSimpleType(L) : AlgLie -> AlgLie
Example AlgLie_SemiSimpleType (H75E8)
Other properties of Lie Algebras
KillingMatrix(L) : AlgLie -> AlgMatElt
AdjointMatrix(L, x) : AlgLie, AlgLieElt -> AlgMatElt
Example AlgLie_Other (H75E9)
NonNilpotentElement(L) : AlgLie -> AlgLieElt
Example AlgLie_NonNilpotentElement (H75E10)