Noncommutative Algebraic Geometry and Representations of Quantized Algebras

This text contains an introduction to the recently developed spectral theory of associative rings and Abelian categories, and its applications to the study of irreducible representations of classes of algebras which play an important part in modern mathematical physics. It is a self-contained volume for researchers and graduate students interested in new geometric ideas in algebra, and in the spectral theory of noncommutative rings, currently invading mathematical physics. It should be useful reading for mathematicians working on representation theory, quantum groups and related topics, noncommutative algebra, algebraic geometry, and algebraic K-theory.