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 algebra over 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 type over the ring \(R\) with Weyl group \(W\). The roots and coroots of \(W\) must have integral components. See Chapter Groups of Lie Type.