MAGMA Computational Algebra System

INTRODUCTION TO LIE THEORY

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;

4.

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

5.

Groups of Lie type (connected reductive algebraic groups);

5.

Representations of Lie algebras and groups of Lie type;

6.

Universal enveloping algebras and Quantum groups.

DETAILS

 
Descriptions of Coxeter Groups

 
Root Systems and Root Data

 
Coxeter and Reflection Groups

 
Lie Algebras and Groups of Lie Type

 
Highest Weight Representations

 
Bibliography

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