INTRODUCTION TO LIE THEORY

A number of structures from Lie theory and the theory of Coxeter groups can now be handled in Magma. Specifically we have facilities 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.

Lie algebras, given as structure constant algebras;

5.

Groups of Lie type.

DETAILS

 
Descriptions of Coxeter Groups

 
Root Systems and Root Data

 
Coxeter and Reflection Groups

 
Bibliography