**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

2001; 304 pp; Softcover

MSC: Primary 17; 81;

**Print ISBN: 978-0-8218-2654-6**

Product Code: MMONO/195

Product Code: MMONO/195

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

**Electronic ISBN: 978-1-4704-4621-5
Product Code: MMONO/195.E**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

# Infinite-Dimensional Lie Algebras

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*Minoru Wakimoto*

This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of \({\widehat {\mathfrak {sl}}}(2, {\mathbb C})\), root systems, the Cartan matrix, and a Dynkin diagram of a finite-dimensional simple Lie algebra. Continuing on, the main subjects of the book are the structure (real and imaginary root systems) of and the character formula for Kac-Moody superalgebras, which is explained in a very general setting. Only elementary linear algebra and group theory are assumed. Also covered is modular property and asymptotic behavior of integrable characters of affine Lie algebras. The exposition is self-contained and includes examples. The book can be used in a graduate-level course on the topic.

#### Readership

Graduate students and research mathematicians interested in Lie algebras and Lie superalgebras.

#### Table of Contents

# Table of Contents

## Infinite-Dimensional Lie Algebras

- Cover Cover11
- Title page v6
- Contents vii8
- Preface ix10
- Preface to the English edition xiii14
- Overview xv16
- Opening 120
- Structures and representations of BKM (super-)algebras 7392
- Affine Lie algebras 153172
- Modular transformations of characters of affine Lie algebras 205224
- Fusion algebras 245264
- In lieu of postscript–Virasoro algebra 253272
- Further developments 285304
- Bibliography 291310
- Index 301320
- Back Cover Back Cover1326