Lie Theory

Lie Theory#

Introduction

Overview of Lie theory in Magma.

Introduction to Lie Theory
Lie Algebras

Structure constants, subalgebras, ideals and derivations.

Lie Algebras
Root Systems

Root systems, Dynkin diagrams and Cartan matrices.

Root Systems
Root Data

Root data, coroots, weights and related constructions.

Root Data
Cartan Matrices

Cartan matrices, Coxeter matrices and Dynkin diagrams.

Cartan Matrices
Coxeter Groups

Coxeter group constructors, word arithmetic and Bruhat order.

Coxeter Groups
Reflection Groups

Real and complex reflection groups and their properties.

Reflection Groups
Chevalley Groups

Groups of Lie type, Borel subgroups and parabolic subgroups.

Chevalley Groups