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Introduction to Finite and Infinite Dimensional Lie (Super)algebras
Including numerous exercises and worked examples, this research monograph systematically describes the formal relationship between Lie Theory and other areas of mathematics and mathematical physics where lie algebras, superalgebras, and other related structures naturally arise
Neelacanta Sthanumoorthy (Author)
9780128046753, Elsevier Science
Hardback, published 11 August 2016
512 pages
22.9 x 15.1 x 3 cm, 0.91 kg
"...it’s a dense book, not meant for neophytes, notwithstanding its many exercises. It is a very good book, I think, and remarkable for its sweep." --MAA Reviews
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.
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
