Algebraic geometry for associative algebras / Freddy van Oystaeyen.

Format:

Book

Author/Creator:

Oystaeyen, F. Van, 1947-

Contributor:

Alumni and Friends Memorial Book Fund.

Series:

Monographs and textbooks in pure and applied mathematics ; 232.

Monographs and textbooks in pure and applied mathematics ; 232

Language:

English

Subjects (All):

Geometry, Algebraic.

Associative algebras.

Algebraic topology.

Schemes (Algebraic geometry).

Grothendieck groups.

Physical Description:

vi, 287 pages : illustrations ; 24 cm.

Place of Publication:

New York : M. Dekker, [2000]

Contents:

Chapter 1 The Noncommutative Site

1.1 Affine Schematic Algebras 5

1.2 Proj and Schematic Algebras 16

1.3 Schemes on the Noncommutative Site 37

Chapter 2 Structure Sheaves and their Sections

2.1 Serre's Global Section Theorem on the Noncommutative Site 53

2.2 The Quantum Site 63

2.3 Quantum Sections. Examples 70

2.4 Almost Commutative Geometry 77

2.4.A Sheaves of Localizations 78

2.4.B Sheaves of Microlocalizations and Quantum Sections 85

2.4.C Quantized Formal Schemes 91

Chapter 3 Regular Algebras

3.1 Some Facts about Dimensions 103

3.2 Regularity Conditions 117

3.3 Short Survey of Results on Low Dimensional Regular Algebras 127

Chapter 4 Valuations and Divisors

4.1 Valuations of Skewfields 139

4.2 Filtrations for Totally Ordered Groups 145

4.3 Valuation Filtrations and Extensions 151

4.4 Reductions of Algebras 158

4.5 Introduction of a Divisor Theory on Weyl Fields 173

Chapter 5 Cohomology Theories

5.1 Cohomology of Schematic Algebras 189

5.2 Cech Cohomology 200

Chapter 6 A Functorial Approach

6.1 Group Objects 207

6.2 Quantum Groups 213

6.3 Multiplicative Matrices 222

6.4 Braided Categories 225

6.5 Some Invariants of Braided Categories and Quantum Groups 235

Chapter 7 Formalizing the Topology

7.1 The Lattice-Type Approach 243

7.2 Skew Grothendieck-Topologies 255

7.3 Elements of Sheaf Theory over Skew Topologies 262.

Notes:

Includes bibliographical references page (271-280) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

082470424X

OCLC:

44507262