內容簡介
本書是一部權威著作。Kac是該領域的創始人和專家，在無限維李
無限維李代數代數和理論物理等領域做出了傑出的貢獻。Kac-Moody代數是近代代數中一個極為重要的分支，在理論物理學、數學物理學及許多數學領域中都有重要的套用。本書詳細討論了無限維李代數中非常重要的Kac-Moody代數的基本理論及其表示理論，全面介紹了Kac-Moody代數在數學和物理學中的套用。書中定理的陳述和證明簡明扼要，各章有大量習題以及提示。
目錄
Introduction.
Notational Conventions
Chapter 1. Basic Definitions
Chapter 2. The lnvariantbilinearForm and the Generalized Casimir Operator
Chapter 3. Integrable Representations of Kac-Moody Algebras and the Weyl Group
Chapter 4. A Classification of GeneralizedcaftanMatrices
Chapter 5. Real and Imaginary Roots
Chapter 6. Affine Algebras: the Normalized Invariant Form， the Root System， and the Weyl Group
Chapter 7. Affine Algebras as Central Extensions of Loop Algebras
Chapter 8. Twisted Affine Algebras and Finite Order Automorphisms
Chapter 9. Highest-Weight Modules over Kac-Moody Algebras
Chapter 10. Integrable Highest-Weight Modules: the Character Formula
Chapter 11. Integrable Highest-Weight Modules: the Weight System and the Unitarizability
Chapter 12. Integrable Highest-Weight Modules over Affine Algebras. Application to η-Function Identities.SugawaraOperators and Branching Functions
Chapter 13. Affine Algebras， Theta Functions， and Modular Forms
Chapter 14. The Principal and Homogeneous Vertex Operator Constructions of the Basic Representation. Boson-fermionCorrespondence. Application to Soliton Equations
Index of Notations and Definitions
References
Conference Proceedings and Collections of Papers
