Lie Theory#

Introduction to Lie Theory

Overview of Lie theory in Magma.

Introduction to Lie Theory
Coxeter Systems

Coxeter matrices, Coxeter graphs, Cartan matrices and Dynkin diagrams.

Coxeter Systems
Root Systems

Root systems, Dynkin diagrams and Cartan matrices.

Root Systems
Root Data

Root data, coroots, weights and related constructions.

Root Data
Coxeter Groups

Coxeter group constructors, word arithmetic and Bruhat order.

Coxeter Groups
Reflection Groups

Real and complex reflection groups and their properties.

Reflection Groups
Lie Algebras

Structure constants, subalgebras, ideals and derivations.

Lie Algebras
Kac-Moody Lie Algebras

Construction and structural invariants of Kac-Moody Lie algebras.

Kac-Moody Lie Algebras
Quantum Groups

Quantized enveloping algebras, their representations and Hopf structure.

Quantum Groups
Groups of Lie Type

Groups of Lie type, Borel subgroups and parabolic subgroups.

Groups of Lie Type
Representations of Lie Groups and Algebras

Highest weight representations of Lie algebras and reductive algebraic groups.

Representations of Lie Groups and Algebras