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Lie Algebras of Finite and Affine Type
Buch von Roger Carter
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
Roger Carter is an Emeritus Professor of Mathematics at the University of Warwick.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2016
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 652
ISBN-13: 9780521851381
ISBN-10: 0521851386
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Carter, Roger
Hersteller: Cambridge University Press
Maße: 235 x 157 x 39 mm
Von/Mit: Roger Carter
Erscheinungsdatum: 07.03.2016
Gewicht: 1,083 kg
preigu-id: 102293984
Über den Autor
Roger Carter is an Emeritus Professor of Mathematics at the University of Warwick.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2016
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 652
ISBN-13: 9780521851381
ISBN-10: 0521851386
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Carter, Roger
Hersteller: Cambridge University Press
Maße: 235 x 157 x 39 mm
Von/Mit: Roger Carter
Erscheinungsdatum: 07.03.2016
Gewicht: 1,083 kg
preigu-id: 102293984
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