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This book 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.
Audience: 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. Valuable reading for mathematicians working on representation theory, quantum groups and related topics, noncommutative algebra, algebraic geometry, and algebraic K-theory.
Preface. I. Noncommutative Affine Schemes. II. The Left Spectrum and Irreducible Representation of 'Small' Quantized and Classical Rings. III. Noncommutative Local Algebra. IV. Noncommutative Local Algebra and Representations of Certain Rings of Mathematical Physics. V. Skew PBW Monads and Representations. VI. Six Spectra and Two Dimensions of an Abelian Category. VII. Noncommutative Projective Spectrum. References. Index of Notations. Index.
Posted March 29, 2012
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