Structure and Representation Theory of Infinite-dimensional Lie Algebras
نویسنده
چکیده
Kac-Moody algebras are a generalization of the finite-dimensional semisimple Lie algebras that have many characteristics similar to the finite-dimensional ones. These possibly infinite-dimensional Lie algebras have found applications everywhere from modular forms to conformal field theory in physics. In this thesis we give two main results of the theory of Kac-Moody algebras. First, we present the classification of affine Kac-Moody algebras by Dynkin diagrams, which extends the Cartan-Killing classification of finite-dimensional semisimple Lie algebras. Second, we prove the Kac Character formula, which a generalization of the Weyl character formula for Kac-Moody algebras. In the course of presenting these results, we develop some theory as well.
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