[Next][Prev] [Right] [____] [Up] [Index] [Root]
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.
Acknowledgements
Descriptions of Coxeter Groups
Root Systems and Root Data
Coxeter and Reflection Groups
Lie Algebras and Groups of Lie Type
Highest Weight Representations
Universal Enveloping Algebras and Quantum Groups
Bibliography
DETAILS
Descriptions of Coxeter Groups
Root Systems and Root Data
Coxeter and Reflection Groups
Lie Algebras and Groups of Lie Type
Highest Weight Representations
Universal Enveloping Algebras and Quantum Groups
Bibliography
[Next][Prev] [Right] [____] [Up] [Index] [Root]
Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012