Introduction to Kac-Moody algebra / Wan Zhe-xian.

Format:

Book

Author/Creator:

Wan, Zhexian.

Language:

English

Subjects (All):

Kac-Moody algebras.

Lie algebras.

Physical Description:

1 online resource (171 p.)

Other Title:

Kac-Moody algebra

Place of Publication:

Singapore ; Teaneck, NJ : World Scientific, c1991.

Language Note:

English

Summary:

This book is an introduction to a rapidly growing subject of modern mathematics, the Kac-Moody algebra, which was introduced by V Kac and R Moody simultanously and independently in 1968.

Contents:

PREFACE; CONTENTS; CHAPTER 1 THE LIE ALGEBRA g(A); 1.1. Realization of a Complex n x n Matrix A; 1.2. Construction of the Lie Algebra g(A); 1.3. Construction of the Lie Algebra g(A)(contunued); 1.4. A Characterization of the Lie Algebra g(A); 1.5. The Derived Algebra g(A) of g(A); 1.6. Center of g(A) and g(A); 1.7. Minimal Number of Generators of g(A); 1.8. The Subalgebra Associated with a Principal Submatrix; 1.9. Decomposability; 1.10. Some Simplicity Propositions; Reference!; CHAPTER 2 CLASSIFICATION OF GENERALIZED CARTAN MATRICES

2.1. A Fundamental Fact from the Theory of Linear Inequalities2.2. Vinberg's Clattiflcatioi Theorem; 2.3 Properties of Matrices of Finite and Affine Types; 2.4. Properties of Generalized Cartan Matrix of Finite or Affine Types; 2.5. Classification of Generalized Cartan Matrices of Finite and Affine Types; 2.6. Classification of Generalized Cartan Matrices of Hyperbolic Type; Additional References; CHAPTER 3 THE INVARIANT BILINEAR FORM; 3.1. The Existence of the Invariant Bilinear Form; 3.2. Uniqueness of the Invariant Bilinear Form

3.3. The Case A Being a Symmetrizable Generalized Cartan Matrix3.4. The Case A Being a Generalized Cartan Matrix of Affline Type; CHAPTER 4 THE WEYL GROUP; 4.1. The Relations Satisfied by the ChevalIey Generators; 4.2. The Weyl Group; 4.3. The Tits Cone; 4.4. The Case of A Being a Symmetrizable Generalized Cartan Matrix; 4.5. Weight Strings; 4.6. Characterization of Kac-Moody Algebra g(A) Associated with a Generalized Cartan Matrix of Finite Type; Additional References; CHAPTER 5 REAL AND IMAGINARY ROOTS; 5.1 Definitions and Elementary Properties

5.2 Kac's Description of the Set of Imaginary Roots5.3 Existence of Imaginary Roots; 5.4 Description of the Set of Short Real, Long Real and Imaginary Roots; 5.5 Root Systems of Affine Lie Algebras; 5.6 The Tits Cone and the Imaginary Cone; 5.7. The Root Base; Additional References; CHAPTER 6 Weyl GROUPS OF AFFINE LIE ALGEBRAS; 6.1. The Weyl Group of an Affine Lie Algebra; 6.2. The Affine Weyl Group; Additional References; CHAPTER 7 REALIZATION OF AFFINE LIE ALGEBRAS; 7.1. Realization of Non-twisted Affine Lie Algebras; 7.2. Realization of Twisted Affine Lie Algebras

CHAPTER 8 INTRODUCTION TO REPRESENTATION THEORY OF KAC-MOODY ALGEBRAS8.1. g(A)-modules, Category O and Formal Characters; 8.2. Generalized Casimir Operator; 8.3 Integrable Highest Weight Modules and Character Formula; Additional References; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789814434485

9814434485

9781299149359

1299149359

OCLC:

828792782