Introduction to finite and infinite dimensional lie (super)algebras - Sthanumoorthy, N. (Neelacanta), 1945- (Amsterdam : Elsevier, 2016)
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 theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras.
2.1 Basic concepts in Kac-Moody algebrasHence for a symmetrizable Cartan matrix, one can give the following definition for Kac-Moody algebra; 2.2 Classification of finite, affine, hyperbolic, and extended-hyperbolic Kac-Moody algebras and their Dynkin diagrams; Properties of Dynkin diagrams; Dynkin diagrams for affine types; Properties of matrices of finite and affine types; For a GCM of affine type, Dynkin diagrams of A and At; Some properties of Dynkin diagrams of hyperbolic types; Some examples of Cartan matrices of hyperbolic types and their Dynkin diagrams.
Online resource; title from PDF title page (EBSCO, viewed May 3, 2016)
Includes bibliographical references and index.
Keywords: Lie algebras; MATHEMATICS / Algebra / Intermediate; Lie algebras; Electronic books