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Infinite-Dimensional Lie Algebras
Infinite-Dimensional Lie Algebras
Date: 24 Dec 2006, 20:21
(Translations of Mathematical Monographs)
Pages: 304

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.


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