Adjoint representation decomposition of finite dimensional simple Lie algebras
The root chain of finite dimensional simple Lie algebras over complex field is given by means of the root space decomposition of finite dimensional simple Lie algebras.By the classifica-tion of irreducible sl(2,C)-modules over complex field,finite dimensional simple Lie algebras y over complex field under adjoint action as sl(2,C)-module is decomposed into a direct sum of irreducible submodule of y.