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Algebraic Geometry for Associative Algebras

Author: Freddy Van Oystaeyen
Publisher: Boca Raton, FL : CRC Press, 2000.
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Edition/Format:   eBook : Document : English : First edition
Summary:
"This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theory that sustains the duality between algebraic geometry and  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Freddy Van Oystaeyen
ISBN: 9781482270525 1482270528
OCLC Number: 1027749812
Description: 1 online resource : text file, PDF
Contents: Cover; Half Title; Title Page; Copyright Page; Preface; Contents; Introduction; Chapter 1 The Noncommutative Site; 1.1 Affine Schematic Algebras; 1.1.1 Example. The generator filtration; 1.1.2 Convention; 1.1.3 Proposition; 1.1.4 Example. Rees Rings of the Weyl Algebras; 1.1.5 Proposition; 1.1.6 Remarks; 1.1.7 Definitions; 1.1.8 Proposition; 1.1.9 Rings of Generic Matrices; 1.1.10 Lemma; 1.1.11 Note; 1.1.12 Examples; 1.1.13 Definition; 1.2 Proj and Schematic Algebras; 1.2.1 Definition; 1.2.2 Lemma; 1.2.3 Lemma; 1.2.4 Proposition; 1.2.5 Theorem; 1.2.6 Corollary; 1.2.7 Proposition 1.2.8 Proposition1.2.9 Proposition; 1.2.10 Corollary; 1.2.11 Example; 1.2.12 Lemma; 1.2.13 Corollary; 1.2.14 Example. Quantum Weyl Algebras; 1.2.15 Lemma; 1.2.16 Lemma; 1.2.17 Proposition; 1.2.18 Remark; 1.2.19 Theorem; 1.2.20 Corollary; 1.2.21 Example: E. Witten's gauge algebras for S U(2); 1.2.22 Theorem; 1.2.23 Example. Quantum Sl 2 (Woronowicz); 1.2.24 Theorem; 1.2.25 Corollary; 1.3 Schemes on the Noncommutative Site; 1.3.1 Lemma; 1.3.2 Lemma (cf . [9], [71]); 1.3.3 Proposition; 1.3.4 Trivial Examples; 1.3.5 Theorem; 1.3.6 Theorem; 1.3.7 Lemma; 1.3.8 Theorem; 1.3.9 Proposition 1.3.10 Definition and Observation1.3.11 Lemma; 1.3.12 Definition; 1.3.13 Definition; 1.3.14 Observation; 1.3.15 Proposition; 1.3.16 Lemma; 1.3.17 Theorem; 1.3.18 Proposition; Chapter 2 Structure Sheaves and their Sections; 2.1 Serre's Global Section Theorem on the Noncommutative Site; 2.1.1 Definition; 2.1.2 Remark; 2.1.3 Example; 2.1.4 Theorem; 2.1.5 Theorem; 2.1.6 Theorem; 2.1.7 Observation; 2.1.8 Proposition; 2.1.9 Proposition; 2.1.10 Proposition; 2.2 The Quantum Site; 2.2.1 Proposition; 2.2.2 Lemma; 2.2.3 Lemma; 2.2.4 Lemma; 2.2.5 Lemma; 2.2.6 Lemma; 2.2.7 Definition; 2.2.8 Theorem 2.2.9 Observation2.2.10 Proposition; 2.2.11 Corollary; 2.2.12 Proposition; 2.2.13 Corollary; 2.3 Quantum Sections. Examples; 2.3.1 The First Weyl Algebra A1 (~); 2.3.2 Quantum Sections of Enveloping Algebras; 2.3.3 Observation; 2.3.4 Example; 2.3.5 Colour Lie Super Algebras; 2.3.6 Theorem; 2.3.7 Quantized Weyl Algebras; 2.4 Almost Commutative Geometry; 2.4.A Sheaves of Localizations; 2.4.1 Lemma; 2.4.2 Corollary; 2.4.3 Proposition; 2.4.4 Corollary; 2.4.5 Theorem; 2.4.6 Theorem; 2.4.7 Observation; 2.4.8 Proposition; 2.4.9 Example; 2.4.10 Theorem; 2.4.11 Corollary; 2.4.12 Proposition 2.4.B Sheaves of Microlocalizations and Quantum Sections2.4.13 Proposition; 2.4.14 Theorem; 2.4.15 Remark; 2.4.16 Theorem; 2.4.17 Corollary; 2.4.18 Example; 2.4.C Quantized Formal Schemes; 2.4.19 Theorem; 2.4.20 Theorem; 2.4.21 Lemma; 2.4.22 Lemma; 2.4.23 Meta-Lemma; 2.4.24 Theorem; 2.4.25 Theorem; Chapter 3 Regular Algebras; 3.1 Some Facts about Dimensions; 3.1.1 Proposition; 3.1.2 Theorem (Change of Rings Theorems); 3.1.3 Theorem (M. Auslander); 3.1.4 Proposition; 3.1.5 Theorem (cf. [71, Theorem 12, p. 68]); 3.1.6 Proposition (Graded Version of Auslander's Theorem)
Series Title: Chapman & Hall/CRC Pure and Applied Mathematics
Responsibility: editor, Freddy Van Oystaeyen.

Abstract:

"This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theory that sustains the duality between algebraic geometry and commutative algebra to the noncommutative level."--Provided by publisher.

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