Algebraic Geometry for Associative Algebras. (2000)

• Record Type: Book
• Further Information: Note: Editor, Freddy Van Oystaeyen.
• Editors: Van Oystaeyen, Freddy
• 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)
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2000
• Extent: 1 online resource
• Subjects: 516.3/5; Algebra; Algebra; Electronic books
• Languages: English
• ISBNs: 9781482270525; 1482270528
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.