Lie Theory#
Introduction
Overview of Lie theory in Magma.
Lie Algebras
Structure constants, subalgebras, ideals and derivations.
Root Systems
Root systems, Dynkin diagrams and Cartan matrices.
Root Data
Root data, coroots, weights and related constructions.
Cartan Matrices
Cartan matrices, Coxeter matrices and Dynkin diagrams.
Coxeter Groups
Coxeter group constructors, word arithmetic and Bruhat order.
Reflection Groups
Real and complex reflection groups and their properties.
Chevalley Groups
Groups of Lie type, Borel subgroups and parabolic subgroups.