Infinite-Dimensional Lie Algebras

This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of root systems, the Cartan matrix, and a Dynkin diagram of a finite-dimensional simple Lie algebra. The main subjects of the book are the structure (real and imaginary root systems) of and the character formula for Kac-Moody superalgebras, which is explained in a very general setting. Only elementary linear algebra and group theory are assumed. Also covered is modular property and asymptotic behavior of integrable characters of affine Lie algebras. The exposition is self-contained and includes examples.