A number of structures from Lie theory and the theory of Coxeter groups can be handled by Magma. Specifically, facilities are provided for:

1.
Coxeter matrices, Coxeter graphs, Cartan matrices, Dynkin diagrams, and Cartan's naming system for Coxeter groups;

2.
Finite root systems and finite root data;

3.
Coxeter groups in three different formats: as finitely presented groups, as permutation groups, and as reflection groups;

4.
Complex reflection groups;

5.
Lie algebras, given as structure constant algebras, matrix algebras, or finitely generated algebras;

6.
Groups of Lie type (connected reductive algebraic groups);

7.
Representations of Lie algebras and groups of Lie type;

8.
Universal enveloping algebras and Quantum groups.

V2.28, 13 July 2023