Lie Theory
==========

.. toctree::
   :hidden:

   Introduction/index-introduction
   LieAlgebras/index-lie-algebras
   RootSystems/index-root-systems
   RootData/index-root-data
   CartanMatrices/index-cartan-matrices
   CoxeterGroups/index-coxeter-groups
   ReflectionGroups/index-reflection-groups
   ChevalleyGroups/index-chevalley-groups

.. grid:: 1 2 3 3
   :gutter: 3
   :class-container: index-topic-grid

   .. grid-item-card:: Introduction
      :link: Introduction/index-introduction
      :link-type: doc

      Overview of Lie theory in Magma.

   .. grid-item-card:: Lie Algebras
      :link: LieAlgebras/index-lie-algebras
      :link-type: doc

      Structure constants, subalgebras, ideals and derivations.

   .. grid-item-card:: Root Systems
      :link: RootSystems/index-root-systems
      :link-type: doc

      Root systems, Dynkin diagrams and Cartan matrices.

   .. grid-item-card:: Root Data
      :link: RootData/index-root-data
      :link-type: doc

      Root data, coroots, weights and related constructions.

   .. grid-item-card:: Cartan Matrices
      :link: CartanMatrices/index-cartan-matrices
      :link-type: doc

      Cartan matrices, Coxeter matrices and Dynkin diagrams.

   .. grid-item-card:: Coxeter Groups
      :link: CoxeterGroups/index-coxeter-groups
      :link-type: doc

      Coxeter group constructors, word arithmetic and Bruhat order.

   .. grid-item-card:: Reflection Groups
      :link: ReflectionGroups/index-reflection-groups
      :link-type: doc

      Real and complex reflection groups and their properties.

   .. grid-item-card:: Chevalley Groups
      :link: ChevalleyGroups/index-chevalley-groups
      :link-type: doc

      Groups of Lie type, Borel subgroups and parabolic subgroups.