無限維李代數(shù)

內(nèi)容概要

本書是一部權(quán)威著作。Kac是該領(lǐng)域的創(chuàng)始人和專家，在無限維李代數(shù)和理論物理等領(lǐng)域做出了杰出的貢獻(xiàn)。    Kac-Moody代數(shù)是近代代數(shù)中一個(gè)極為重要的分支，在理論物理學(xué)、數(shù)學(xué)物理學(xué)及許多數(shù)學(xué)領(lǐng)域中都有重要的應(yīng)用。本書詳細(xì)討論了無限維李代數(shù)中非常重要的Kac-Moody代數(shù)的基本理論及其表示理論，全面介紹了Kac-Moody代數(shù)在數(shù)學(xué)和物理學(xué)中的應(yīng)用。書中定理的陳述和證明簡明扼要，各章有大量習(xí)題以及提示。

書籍目錄

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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