Related Structures

In this section functions for creating other structures from a permutation Coxeter group are briefly listed. See the appropriate chapters of the Handbook for more details.

CoxeterGroup(GrpFP, W) : Cat, GrpPermCox -> GrpFPCox

Presentation(W) : GrpPermCox -> GrpFPCox

The finitely presented group isomorphic to the permutation Coxeter group W. See Chapter FINITELY PRESENTED GROUPS.

ReflectionGroup(W) : GrpPermCox -> GrpMat

CoxeterGroup(GrpMat, W) : Cat, GrpPermCox -> GrpFPCox

The reflection group isomorphic to the Coxeter group W. See Chapter REFLECTION GROUPS.

LieAlgebra(W, R) : GrpPermCox, Rng -> AlgLie

The reductive Lie algebraover the ring R with Weyl group W. If W is noncrystallographic, an error is flagged. See Section Almost Reductive Lie Algebras.

GroupOfLieType(W, R) : GrpPermCox, Rng -> GrpLie

The group of Lie typeover the ring R with Weyl group W. The roots and coroots of W must have integral components. See Chapter GROUPS OF LIE TYPE.