MAGMA Computational Algebra System

Related Structures

In this section we briefly list functions for creating other structures from a reflection 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.

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

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

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

The reductive Lie algebraover the ring R with Weyl group W. Unless W is finite, real, and crystallographic, an error is flagged. See Section Almost Reductive Lie Algebras.

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

The group of Lie typeover 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.