Translations of Mathematical Monographs Iwanami Series in Modern Mathematics 2001; 304 pp; softcover Volume: 195 ISBN10: 0821826549 ISBN13: 9780821826546 List Price: US$65 Member Price: US$52 Order Code: MMONO/195
 This volume begins with an introduction to the structure of finitedimensional simple Lie algebras, including the representation of \({\widehat {\mathfrak {sl}}}(2, {\mathbb C})\), root systems, the Cartan matrix, and a Dynkin diagram of a finitedimensional 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 KacMoody 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 selfcontained and includes examples. The book can be used in a graduatelevel course on the topic. Readership Graduate students and research mathematicians interested in Lie algebras and Lie superalgebras. Table of Contents  Opening
 Structures and representations of BKM (super)algebras
 Affine Lie algebras
 Modular transformations of characters of affine Lie algebras
 Fusion algebras
 In lieu of postscriptVirasoro algebra
 Further developments
 Bibliography
 Index
