Finite Groups of Lie Type

We have implemented code for computing in non-groups of Lie type, with elements represented by their Bruhat decomposition. These groups can be defined over any Magma ring. The twisted groups will be implemented in a future release, but for now it is possible to compute with them by treating them as subgroups of the non-twisted groups.

The standard and regular (adjoint) representations for each group may be computed.

• Generators for all classical families of groups of Lie type over a finite field.
• Generators for all exceptional families of groups of Lie type over a finite field.
• Killing form of the Cartan algebra associated with a given Weyl group
• Root elements
• Fundamental roots and their negatives of a simple Lie algebra of given type and rank
• Lie algebra of a Chevalley group as a structure constant algebra
• Adjoint action
• Graph automorphism of a Coxeter group
• Degree of a representation with specified weight
• The BN-pair for a Chevalley group