Kac-Moody（卡茨-穆迪）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
维克多·卡茨著的《无穷维李代数（第3版）（英文版）》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。
本书适合大学数学系高年级本科生、研究生，以及相关专业的研究人员阅读参考。

Introduction
Notational Conventions
Chapter 1. Basic Definitions
Chapter 2. The Invariant Bilinear Form and the Generalized
Casimir Operator
Chapter 3. Integrable Representations of Kac-Moody Algebras
sad the Weyl Group
Chapter 4. A Classification of Generalized Cartsa Matrices
Chapter 5. Real sad Imaginary Roots
Chapter 6. Affine Algebras: the Normalized Invariant
Form, the Root System, sad the Weyl Group
Chapter 7. Afflne Algebras as Central Extensions of
Loop Algebras
Chapter 8. Twisted Atllne 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 Aitine
Algebras. Application to r/-Function Identities.
Sugawara Operators and Branching Functions
Chapter 13. Afline Algebras, Theta Functions, sad 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 sad Definitions
References
Conference Proceedings and Collections of Papers
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