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Infinite dimensional Lie algebras: an introduction

✍ Scribed by Victor G. Kac

Book ID
127434987
Publisher
Birkhäuser
Year
1984
Tongue
English
Weight
4 MB
Series
Progress in Mathematics
Edition
1983
Category
Library
ISBN
0817631186

No coin nor oath required. For personal study only.

✦ Synopsis

This is the third, substantially revised edition of this important monograph by a giant in the field of mathematics. The book is concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. Each chapter begins with a motivating discussion and ends with a collection of exercises with hints to the more challenging problems. The theory has applications in many areas of mathematics, and Lie algebras have been significant in the study of fundamental particles, including string theory, so this book should appeal to mathematical physicists, as well as mathematicians.

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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