Roger Carter

Lie Algebras of Finite and Affine Type

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 652
• Erscheinungstermin: 7. März 2016
• Englisch
• Abmessung: 235mm x 157mm x 39mm
• Gewicht: 1083g
• ISBN-13: 9780521851381
• ISBN-10: 0521851386
• Artikelnr.: 21449664

Autorenporträt

Roger Carter is an Emeritus Professor of Mathematics at the University of Warwick.

Inhaltsangabe

1. Basic concepts
2. Representations of soluble and nilpotent Lie algebras
3. Cartan subalgebras
4. The Cartan decomposition
5. The root systems and the Weyl group
6. The Cartan matrix and the Dynkin diagram
7. The existence and uniqueness theorems
8. The simple Lie algebras
9. Some universal constructions
10. Irreducible modules for semisimple Lie algebras
11. Further properties of the universal enveloping algebra
12. Character and dimension formulae
13. Fundamental modules for simple Lie algebras
14. Generalized Cartan matrices and Kac-Moody algebras
15. The classification of generalised Cartan matrices
16 The invariant form, root system and Weyl group
17. Kac-Moody algebras of affine type
18. Realisations of affine Kac-Moody algebras
19. Some representations of symmetrisable Kac-Moody algebras
20. Representations of affine Kac-Moody algebras
21. Borcherds Lie algebras
Appendix.