Introduction to Finite and Infinite Dimensional Lie (Super)algebras

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations.

The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras.

Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theoryClosely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identitiesIncludes numerous tables of the properties of individual Lie algebras and Lie superalgebrasFocuses on Kac-Moody algebras

1. Finite dimensional Lie Algebras

2. Kac-Moody algebras

3. Generalized Kac-Moody algebras

4. Lie superalgebras

5. Borcherds Kac-Moody Lie superalgebras

6. Lie algebras of Lie groups, Kac-Moody groups, supergroups and some specialized topics in finite and infinite dimensional Lie algebras