无限维李代数

2006-4  

世界图书出版公司北京  

VICTOR G.KAC  

400  

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本书是一部权威著作。Kac是该领域的创始人和专家，在无限维李代数和理论物理等领域做出了杰出的贡献。 Kac-Moody代数是近代代数中一个极为重要的分支，在理论物理学、数学物理学及许多数学领域中都有重要的应用。本书详细讨论了无限维李代数中非常重要的Kac-Moody代数的基本理论及其表示理论，全面介绍了Kac-Moody代数在数学和物理学中的应用。书中定理的陈述和证明简明扼要，各章有大量习题以及提示。

Introduction. Notational Conventions Chapter 1. Basic Definitions Chapter 2. The lnvariant Bilinear Form and the Generalized Casimir Operator Chapter 3. Integrable Representations of Kac-Moody Algebras and the Weyl Group Chapter 4. A Classification of Generalized Caftan Matrices 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. Sugawara Operators 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-Fermion Correspondence. Application to Soliton Equations Index of Notations and Definitions References Conference Proceedings and Collections of Papers

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