Infinite-dimensional Lie algebras / Minoru Wakimoto ; translated by Kenji Iohara.

Format:

Book

Author/Creator:

Wakimoto, Minoru, 1942-

Series:

Iwanami series in modern mathematics

Translations of mathematical monographs 0065-9282 ; v. 195.

Translations of mathematical monographs, 0065-9282 ; v. 195

Standardized Title:

Mugen jigen Lie-kan. English

Language:

English

Japanese

Subjects (All):

Lie algebras.

Physical Description:

xviii, 304 pages : illustrations ; 22 cm.

Place of Publication:

Providence, RI : American Mathematical Society, [2001]

Contents:

1.2. Representation Theory of sl(2, C) 20

1.3. Structure of Simple Finite-Dimensional Lie Algebras 27

1.4. Toward Infinite-Dimensional Lie Algebras 47

1.5. A Few Words on Lie Superalgebras 50

Chapter 2. Structuress and Representations of BKM (Super-) Algebras 73

2.1. Inner Product and Cartan Matrix of BKM (Super-) Algebras 74

2.2. Weyl Groups 100

2.3. Root Systems 110

2.4. Integrable Representations 120

2.5. Character Formulae and Denominator Identity 137

Chapter 3. Affine Lie Algebras 153

3.1. Properties of Weyl Groups and Roots for Simple Finite-Dimensional Lie Algebras 153

3.2. Invariant Form on Simple Finite-Dimensional Lie Algebras 166

3.3. Structure of Affine Lie Algebras 170

3.4. Pairing and Contravariant Form on Verma Modules 183

3.5. Weyl Group of Affine Lie Algebras and Characters of Irreducible Representations 192

3.6. The Jacobi Triple Product Identity 200

Chapter 4. Modular Transformations of Characters of Affine Lie Algebras 205

4.1. Classical Theta Functions 205

4.2. Jacobi's Theta Function - Modular Transformations and Asymptotic Behavior 212

4.3. Modular Transformations of Characters 224

Chapter 5. Fusion Algebras 245

Chapter 6. In Lieu of Postscript - Virasoro Algebra - 253

Further Developments 285.

Notes:

Includes bibliographical references (pages 291-299) and index.

ISBN:

0821826549

OCLC:

44885164