Subgroup Definition Stabiliser Definition Stabiliser Subgroup Theorem Theorem #5000 Dynkin Diagram Determines the Finite-Type Cartan Matrix Algebra Isomorphism Iff Linear Bijection Linear Algebra Symmetric Bilinear Form Iff Symmetric Matrix Linear Algebra Transposition Decomposition Group Theory Central Character Values Are Algebraic Integers Representation Theory Chain Homotopic Maps Induce the Same Homomorphism on Homology Algebra Isomorphism Is an Equivalence Relation Representation Theory Classification Theorem for Finite-Dimensional Simple Lie Algebras Algebra Algebra Area