This is an introduction to the theory of affine Lie algebras, to
the theory of quantum groups, and to the interrelationships between
these two fields that are encountered in conformal field theory.
The description of affine algebras covers the classification
problem, the connection with loop algebras, and representation
theory including modular properties. The necessary background from
the theory of semisimple Lie algebras is also provided. The
discussion of quantum groups concentrates on deformed enveloping
algebras and their representation theory, but other aspects such as
R-matrices and matrix quantum groups are also dealt with. This book
will be of interest to researchers and graduate students in
theoretical physics and applied mathematics.
General
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