Sinossi
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.
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Contenuti
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.
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Noncommutative Algebraic Geometry and Representations of Quantized Algebras
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Springer Netherlands, 1995
ISBN 10: 0792335759
ISBN 13: 9780792335757
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Condizione: Gut. Zustand: Gut | Seiten: 340 | Sprache: Englisch | Produktart: Bücher | This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others. Codice articolo 3031556/203
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Noncommutative Algebraic Geometry and Representations of Quantized Algebras (Mathematics and Its Applications, 330)
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Noncommutative Algebraic Geometry and Representations of Quantized Algebras
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Springer Netherlands Jun 1995, 1995
ISBN 10: 0792335759
ISBN 13: 9780792335757
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others. 340 pp. Englisch. Codice articolo 9780792335757
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It i. Codice articolo 5967493
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