Search results for "Dynkin diagram"

Representations of Affine Kac-Moody Algebras

1989

In the first chapter we explained how simple finite-dimensional Lie algebras can be completely characterized in terms of their Cartan matrices or Dynkin diagrams. The same holds for an arbitrary semisim-ple finite-dimensional Lie algebra. A semisimple Lie algebra is a direct sum of simple ideals which are pairwise orthogonal with respect to the Killing form. It follows that the Cartan matrix of a semisimple Lie algebra decomposes to a block diagonal form, each block representing a simple ideal. Similarly, the Dynkin diagram is a disconnected union of Dynkin diagrams of simple Lie algebras. Next we shall study certain infinite-dimensional Lie algebras which have many similarities with the si…