Book contents
- Frontmatter
- Contents
- Preface
- 1 Basic concepts
- 2 Representations of soluble and nilpotent Lie algebras
- 3 Cartan subalgebras
- 4 The Cartan decomposition
- 5 The root system 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 Generalised Cartan matrices and Kac–Moody algebras
- 15 The classification of generalised Cartan matrices
- 16 The invariant form, Weyl group and root system
- 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
- Notation
- Bibliography of books on Lie algebras
- Bibliography of articles on Kac–Moody algebras
- Index
8 - The simple Lie algebras
Published online by Cambridge University Press: 25 January 2010
Book contents
- Frontmatter
- Contents
- Preface
- 1 Basic concepts
- 2 Representations of soluble and nilpotent Lie algebras
- 3 Cartan subalgebras
- 4 The Cartan decomposition
- 5 The root system 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 Generalised Cartan matrices and Kac–Moody algebras
- 15 The classification of generalised Cartan matrices
- 16 The invariant form, Weyl group and root system
- 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
- Notation
- Bibliography of books on Lie algebras
- Bibliography of articles on Kac–Moody algebras
- Index
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- Lie Algebras of Finite and Affine Type , pp. 121 - 151Publisher: Cambridge University PressPrint publication year: 2005