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Lie Algebras of Finite and Affine Type

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ISBN-10: 0521851386

ISBN-13: 9780521851381

Edition: 2005

Authors: Roger Carter, B. Bollobas, W. Fulton, A. Katok, F. Kirwan

List price: $134.99
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Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject, including both the Cartan-Killing-Weyl theory of finite dimensional simple algebras and the more modern theory of Kac-Moody algebras. Proofs are given in detail and the only prerequisite is a sound knowledge of linear algebra. The Appendix provides a summary of the basic properties of each Lie algebra of finite and affine type.
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Book details

List price: $134.99
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 10/27/2005
Binding: Hardcover
Pages: 650
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 2.552
Language: English

Basic concepts
Representations of soluble and nilpotent Lie algebras
Cartan subalgebras
The Cartan decomposition
The root systems and the Weyl group
The Cartan matrix and the Dynkin diagram
The existence and uniqueness theorems
The simple Lie algebras
Some universal constructions
Irreducible modules for semisimple Lie algebras
Further properties of the universal enveloping algebra
Character and dimension formulae
Fundamental modules for simple Lie algebras
Generalized Cartan matrices and Kac-Moody algebras
The classification of generalised Cartan matrices
The invariant form, root system and Weyl group
Kac-Moody algebras of affine type
Realisations of affine Kac-Moody algebras
Some representations of symmetrisable Kac-Moody algebras
Representations of affine Kac-Moody algebras
Borcherds Lie algebras