Noncommutative algebraic geometry and representations of quantized algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1995
|
| Series: | Mathematics and its applications
330 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 315 S. |
| ISBN: | 0792335759 9789048145775 |
Staff View
MARC
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| 245 | 1 | 0 | |a Noncommutative algebraic geometry and representations of quantized algebras |c by Alexander L. Rosenberg |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 1995 | |
| 300 | |a XII, 315 S. | ||
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| 490 | 1 | |a Mathematics and its applications |v 330 | |
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| 650 | 7 | |a Algèbres non commutatives |2 ram | |
| 650 | 7 | |a Géométrie algébrique |2 ram | |
| 650 | 7 | |a Représentations d'algèbres |2 ram | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Noncommutative algebras | |
| 650 | 4 | |a Representations of algebras | |
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Record in the Search Index
| _version_ | 1804124867571744768 |
|---|---|
| adam_text | TABLE OF CONTENTS
Preface ix
Chapter I
Noncommutative affine schemes 1
Introduction 1
0. Preliminaries: localizations and radical filters 2
1. Left spectrum 4
2. Localizations and the left spectrum 10
3. Morphisms of left spectra 12
4. The left spectrum and the Levitzki radical 16
5. The Levitzki spectrum and the left spectrum 19
6. Structure presheaves. Reconstruction of modules 22
7. Affine and quasi affine schemes. Projective spectra 31
Complementary facts and examples 44
Cl. The left spectrum of a principal domain 44
C2. Left normal morphisms and quantum plane 46
Chapter II
The left spectrum and irreducible representations of small quantized and
classical rings 48
Introduction 48
0. Preliminaries: the spectrum of an abelian category 50
1. The left spectrum of the ring of skew polynomials. Quantum plane 51
2. Restricted skew polynomial rings 58
3. The left spectrum and the irreducible representations of hyperbolic rings 59
4. Applications to basic examples 73
Complementary facts and examples 83
Cl. Hyperbolic rings of Af(2) type 84
C2. Quantum Heisenberg algebra 91
C3. Rings of £/(s/(2)) type 98
C4. Other examples of hyperbolic rings 99
Chapter III
Noncommutative local algebra 110
Introduction HO
vi
1. The spectrum of an abelian category Ill
2. The spectrum and exact localizations 112
3. Local abelian categories and localization at points of the spectrum 117
4. The left spectrum of a ring 119
5. Supports and localizing subcategories 121
6. Left closed subcategories and Zariski topology 124
7. Some other canonical topologies 133
8. Associated points 136
9. Relative spectra 139
Complementary facts and examples 141
Cl. The prime spectrum of an abelian category 141
Chapter IV
Noncommutative local algebra and representations of certain rings of
mathematical physics 142
Introduction 142
1. Quantized Weyl and Heisenberg algebras and hyperbolic rings 143
2. Skew polynomial categories 145
3. The skew Laurent categories 149
4. A part of the spectrum of a skew polynomial category 150
5. The hyperbolic categories 153
6. The spectrum of a hyperbolic category 159
Complementary facts and examples 176
Cl. Hyperbolic categories of higher rank 176
C2. Rings and categories of Heisenberg and Weyl types 178
Chapter V
Skew PBW monads and representations 188
Introduction 188
1. The spectrum of a quasi exact category 190
2. From hyperbolic rings to PBW monads 192
3. Preparation 198
4. Graded monads and modules 199
5. The spectrum of the category of X graded modules 204
6. The spectrum of the category of modules over a PBW monad 208
Complementary facts and examples 214
Cl. Morphisms of graded monads and the spectrum 214
C2. Quasi holonomic modules and characters 215
C3. Dualization 222
C4. Weyl algebras 224
C5. A remark about relations between the spectrum of reductive and (quantized)
Kac Moody Lie algebras and the spectrum of certain hyperbolic rings 231
C6. Two parameter deformations of Af(2) and GL(2) 233
vii
Chapter VI
Six spectra and two dimensions of an abelian category 238
Introduction 238
1. The complete spectrum of an abelian category 239
2. The flat spectrum 249
3. The Goldman spectrum 255
4. The flat spectrum and injective objects 257
5. Injective spectra 262
6. The Gabriel Krull dimension 266
Chapter VII
Noncommutative Projective Spectrum 276
Introduction 276
1. Quasi schemes. Affine morphisms. Subschemes 276
2. Projective spectra 282
3. Affine fibers and projective fibers 290
4. Blowing up and related constructions 294
5. Generalizations. Quantized flag varieties 296
Complementary facts and examples 298
Cl. Relative quasi schemes 298
C2. Quasi schemes with an ample auto equivalence and Pro]. 299
C3. Schemes with ample families of line bundles and generalized Proj. 304
Reference 306
Index of Notations 310
Index 314
|
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| id | DE-604.BV010434779 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:52:29Z |
| institution | BVB |
| isbn | 0792335759 9789048145775 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006953410 |
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| owner_facet | DE-12 DE-739 DE-19 DE-BY-UBM DE-11 |
| physical | XII, 315 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Rosenberg, Alexander L. Verfasser aut Noncommutative algebraic geometry and representations of quantized algebras by Alexander L. Rosenberg Dordrecht [u.a.] Kluwer Acad. Publ. 1995 XII, 315 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 330 Hier auch später erschienene, unveränderte Nachdrucke Algèbres non commutatives ram Géométrie algébrique ram Représentations d'algèbres ram Geometry, Algebraic Noncommutative algebras Representations of algebras Nichtkommutative Algebra (DE-588)4304013-5 gnd rswk-swf Nichtkommutative Algebra (DE-588)4304013-5 s DE-604 Mathematics and its applications 330 (DE-604)BV008163334 330 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006953410&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosenberg, Alexander L. Noncommutative algebraic geometry and representations of quantized algebras Mathematics and its applications Algèbres non commutatives ram Géométrie algébrique ram Représentations d'algèbres ram Geometry, Algebraic Noncommutative algebras Representations of algebras Nichtkommutative Algebra (DE-588)4304013-5 gnd |
| subject_GND | (DE-588)4304013-5 |
| title | Noncommutative algebraic geometry and representations of quantized algebras |
| title_auth | Noncommutative algebraic geometry and representations of quantized algebras |
| title_exact_search | Noncommutative algebraic geometry and representations of quantized algebras |
| title_full | Noncommutative algebraic geometry and representations of quantized algebras by Alexander L. Rosenberg |
| title_fullStr | Noncommutative algebraic geometry and representations of quantized algebras by Alexander L. Rosenberg |
| title_full_unstemmed | Noncommutative algebraic geometry and representations of quantized algebras by Alexander L. Rosenberg |
| title_short | Noncommutative algebraic geometry and representations of quantized algebras |
| title_sort | noncommutative algebraic geometry and representations of quantized algebras |
| topic | Algèbres non commutatives ram Géométrie algébrique ram Représentations d'algèbres ram Geometry, Algebraic Noncommutative algebras Representations of algebras Nichtkommutative Algebra (DE-588)4304013-5 gnd |
| topic_facet | Algèbres non commutatives Géométrie algébrique Représentations d'algèbres Geometry, Algebraic Noncommutative algebras Representations of algebras Nichtkommutative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006953410&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT rosenbergalexanderl noncommutativealgebraicgeometryandrepresentationsofquantizedalgebras |