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