Related Structures

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

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

The Coxeter group isomorphic to the real reflection group W. See Chapter COXETER GROUPS AS PERMUTATION GROUPS.

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

The permutation Coxeter group isomorphic to the finite real reflection group W. See Chapter COXETER GROUPS AS PERMUTATION GROUPS.

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

The reductive Lie algebra over the ring R with Weyl group W. Unless W is finite, real, and crystallographic, an error is flagged. See Section Construction of Semisimple and Reductive Lie Algebras.

GroupOfLieType( W, k ) : GrpMat, Rng -> GrpLie

The group of Lie type over the field k with Weyl group W. Unless W is finite, real, and crystallographic, an error is flagged. The roots and coroots of W must also have integral components. See Chapter GROUPS OF LIE TYPE