# Lie Theory

Introduction to Lie TheoryOverview of Lie theory in Magma.

[Introduction to Lie Theory](Introduction/index-introduction.md)Coxeter SystemsCoxeter matrices, Coxeter graphs, Cartan matrices and Dynkin diagrams.

[Coxeter Systems](CoxeterSystems/index-coxeter-systems.md)Root SystemsRoot systems, Dynkin diagrams and Cartan matrices.

[Root Systems](RootSystems/index-root-systems.md)Root DataRoot data, coroots, weights and related constructions.

[Root Data](RootData/index-root-data.md)Coxeter GroupsCoxeter group constructors, word arithmetic and Bruhat order.

[Coxeter Groups](CoxeterGroups/index-coxeter-groups.md)Reflection GroupsReal and complex reflection groups and their properties.

[Reflection Groups](ReflectionGroups/index-reflection-groups.md)Lie AlgebrasStructure constants, subalgebras, ideals and derivations.

[Lie Algebras](LieAlgebras/index-lie-algebras.md)Kac-Moody Lie AlgebrasConstruction and structural invariants of Kac-Moody Lie algebras.

[Kac-Moody Lie Algebras](KacMoodyLieAlgebras/index-kac-moody-lie-algebras.md)Quantum GroupsQuantized enveloping algebras, their representations and Hopf structure.

[Quantum Groups](QuantumGroups/index-quantum-groups.md)Groups of Lie TypeGroups of Lie type, Borel subgroups and parabolic subgroups.

[Groups of Lie Type](ChevalleyGroups/index-chevalley-groups.md)Representations of Lie Groups and AlgebrasHighest weight representations of Lie algebras and reductive algebraic groups.

[Representations of Lie Groups and Algebras](RepresentationsOfLieGroupsAndAlgebras/index-representations-of-lie-groups-and-algebras.md)