Semi-simple Lie Algebras and Their Representations

a₁ adjoint representation anti-symmetric product B₁ bilinear invariant C₁ calculate Cartan matrix Cartan subalgebra Casimir operator Chapter commutation relations conjugacy classes consider corresponding define determine diagonal dimension Dynkin coefficients Dynkin diagram eigenvalue eigenvector eight dimensional elements of H embedding example formula full algebra G₂ integers invariant bilinear form irreducible component irreducible representation JACOBSON Killing form Lecture Note linear combinations linearly independent M₁ mapping maximal S-subalgebras maximal semi-simple subalgebras Note and Reprint obtained orthogonal positive roots product representation regular subalgebra representation of G representation of SU(2 representation whose highest representation with highest Reprint Volume root space root vectors scalar product semi-simple Lie algebras simple Lie algebra simple roots SU(n subspace Suppose t₂ tation Theory three dimensional representation three-by-three traceless V₁ V₂ vector space weight space weight vector Weyl group zero αι απ ΕΣ