Quadratic algebras:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2005]
|
| Schriftenreihe: | University lecture series
Volume 37 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 159 Seiten |
| ISBN: | 0821838342 9780821838341 |
Internformat
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| 100 | 1 | |a Polishchuk, Alexander |d 1971- |e Verfasser |0 (DE-588)1146424566 |4 aut | |
| 245 | 1 | 0 | |a Quadratic algebras |c Alexander Polishchuk ; Leonid Positselski |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2005] | |
| 264 | 4 | |c © 2005 | |
| 300 | |a xii, 159 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a University lecture series |v Volume 37 | |
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| 700 | 1 | |a Positselski, Leonid |d 1973- |e Verfasser |0 (DE-588)1013551435 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-014170866 | ||
Datensatz im Suchindex
| _version_ | 1804134561631698944 |
|---|---|
| adam_text | Contents
Introduction vii
Chapter 1. Preliminaries 1
0. Conventions and notation 1
1. Bar constructions 2
2. Quadratic algebras and modules 6
3. Diagonal eohomology 7
4. Minimal resolutions 7
5. Low dimensional eohomology 9
6. Lattices and distributivity 11
7. Lattices of vector spaces 15
Chapter 2. Koszul algebras and modules 19
1. Koszulness 19
2. Hilbert series 21
3. Koszul complexes 25
4. Distributivity and n Koszulness 29
5. Homomorphisms of algebras and Koszulness. I 32
6. Homomorphisms of algebras and Koszulness. II 37
7. Koszul algebras in algebraic geometry 40
8. Infinitesimal Hopf algebra associated with a Koszul algebra 45
9. Koszul algebras and monoidal functors 49
10. Relative Koszulness of modules 53
Chapter 3. Operations on graded algebras and modules 55
1. Direct sums, free products and tensor products 55
2. Segre products and Veronese powers. I 59
3. Segre products and Veronese powers. II 63
4. Internal cohomomorphism 68
5. Koszulness cannot be checked using Hilbert series 77
Chapter 4. Poincare Birkhoff Witt Bases 81
1. PBW bases 81
2. PBW theorem 82
3. PBW bases and Koszulness 84
4. PBW bases and operations on quadratic algebras 85
5. PBW bases and distributing bases 86
6. Hilbert series of PBW algebras 87
7. Filtrations on quadratic algebras 88
8. Commutative PBW bases 91
V
vi CONTENTS
9. Z algebras 95
10. Z PBW bases 96
11. Three dimensional Sklyanin algebras 98
Chapter 5. Nonhomogeneous Quadratic Algebras 101
1. Jacobi identity 101
2. Nonhomogeneous PBW theorem 103
3. Nonhomogeneous quadratic modules 104
4. Nonhomogeneous quadratic duality 105
5. Examples 108
6. Nonhomogeneous duality and cohomology 111
7. Bar construction for CDG algebras and modules 112
8. Homology of completed cobar complexes 117
Chapter 6. Families of quadratic algebras and Hilbert series 119
1. Openness of distributivity 119
2. Deformations of Koszul algebras 120
3. Upper bound for the number of Koszul Hilbert series 122
4. Generic quadratic algebras 123
5. Examples with small dim^i and dimA2 125
6. Koszulness is not constructible 127
7. Families of quadratic algebras over schemes 128
Chapter 7. Hilbert series of Koszul algebras and one dependent processes 133
1. Conjectures on Hilbert series of Koszul algebras 133
2. Koszul inequalities 135
3. Koszul duality and inequalities 138
4. One dependent processes 139
5. PBW algebras and two block factor processes 142
6. Operations on one dependent processes 143
7. Hilbert space representations of one dependent processes 146
8. Hilbert series of one dependent processes 147
9. Hermitian construction of one dependent processes 149
10. Modules over one dependent processes 151
Appendix A. DG algebras and Massey products 153
Bibliography 155
|
| adam_txt |
Contents
Introduction vii
Chapter 1. Preliminaries 1
0. Conventions and notation 1
1. Bar constructions 2
2. Quadratic algebras and modules 6
3. Diagonal eohomology 7
4. Minimal resolutions 7
5. Low dimensional eohomology 9
6. Lattices and distributivity 11
7. Lattices of vector spaces 15
Chapter 2. Koszul algebras and modules 19
1. Koszulness 19
2. Hilbert series 21
3. Koszul complexes 25
4. Distributivity and n Koszulness 29
5. Homomorphisms of algebras and Koszulness. I 32
6. Homomorphisms of algebras and Koszulness. II 37
7. Koszul algebras in algebraic geometry 40
8. Infinitesimal Hopf algebra associated with a Koszul algebra 45
9. Koszul algebras and monoidal functors 49
10. Relative Koszulness of modules 53
Chapter 3. Operations on graded algebras and modules 55
1. Direct sums, free products and tensor products 55
2. Segre products and Veronese powers. I 59
3. Segre products and Veronese powers. II 63
4. Internal cohomomorphism 68
5. Koszulness cannot be checked using Hilbert series 77
Chapter 4. Poincare Birkhoff Witt Bases 81
1. PBW bases 81
2. PBW theorem 82
3. PBW bases and Koszulness 84
4. PBW bases and operations on quadratic algebras 85
5. PBW bases and distributing bases 86
6. Hilbert series of PBW algebras 87
7. Filtrations on quadratic algebras 88
8. Commutative PBW bases 91
V
vi CONTENTS
9. Z algebras 95
10. Z PBW bases 96
11. Three dimensional Sklyanin algebras 98
Chapter 5. Nonhomogeneous Quadratic Algebras 101
1. Jacobi identity 101
2. Nonhomogeneous PBW theorem 103
3. Nonhomogeneous quadratic modules 104
4. Nonhomogeneous quadratic duality 105
5. Examples 108
6. Nonhomogeneous duality and cohomology 111
7. Bar construction for CDG algebras and modules 112
8. Homology of completed cobar complexes 117
Chapter 6. Families of quadratic algebras and Hilbert series 119
1. Openness of distributivity 119
2. Deformations of Koszul algebras 120
3. Upper bound for the number of Koszul Hilbert series 122
4. Generic quadratic algebras 123
5. Examples with small dim^i and dimA2 125
6. Koszulness is not constructible 127
7. Families of quadratic algebras over schemes 128
Chapter 7. Hilbert series of Koszul algebras and one dependent processes 133
1. Conjectures on Hilbert series of Koszul algebras 133
2. Koszul inequalities 135
3. Koszul duality and inequalities 138
4. One dependent processes 139
5. PBW algebras and two block factor processes 142
6. Operations on one dependent processes 143
7. Hilbert space representations of one dependent processes 146
8. Hilbert series of one dependent processes 147
9. Hermitian construction of one dependent processes 149
10. Modules over one dependent processes 151
Appendix A. DG algebras and Massey products 153
Bibliography 155 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV020849130 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:19:16Z |
| indexdate | 2024-07-09T20:26:34Z |
| institution | BVB |
| isbn | 0821838342 9780821838341 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014170866 |
| oclc_num | 633570521 |
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| physical | xii, 159 Seiten |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Polishchuk, Alexander 1971- Verfasser (DE-588)1146424566 aut Quadratic algebras Alexander Polishchuk ; Leonid Positselski Providence, Rhode Island American Mathematical Society [2005] © 2005 xii, 159 Seiten txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 37 Quadratischer Körper (DE-588)4667267-9 gnd rswk-swf Kommutativer Ring (DE-588)4164825-0 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Assoziativer Ring (DE-588)4143228-9 gnd rswk-swf Quadratischer Körper (DE-588)4667267-9 s Assoziativer Ring (DE-588)4143228-9 s Kommutativer Ring (DE-588)4164825-0 s Stochastischer Prozess (DE-588)4057630-9 s b DE-604 Positselski, Leonid 1973- Verfasser (DE-588)1013551435 aut Erscheint auch als Online-Ausgabe 978-1-4704-2182-3 University lecture series Volume 37 (DE-604)BV004153846 37 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014170866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Polishchuk, Alexander 1971- Positselski, Leonid 1973- Quadratic algebras University lecture series Quadratischer Körper (DE-588)4667267-9 gnd Kommutativer Ring (DE-588)4164825-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Assoziativer Ring (DE-588)4143228-9 gnd |
| subject_GND | (DE-588)4667267-9 (DE-588)4164825-0 (DE-588)4057630-9 (DE-588)4143228-9 |
| title | Quadratic algebras |
| title_auth | Quadratic algebras |
| title_exact_search | Quadratic algebras |
| title_exact_search_txtP | Quadratic algebras |
| title_full | Quadratic algebras Alexander Polishchuk ; Leonid Positselski |
| title_fullStr | Quadratic algebras Alexander Polishchuk ; Leonid Positselski |
| title_full_unstemmed | Quadratic algebras Alexander Polishchuk ; Leonid Positselski |
| title_short | Quadratic algebras |
| title_sort | quadratic algebras |
| topic | Quadratischer Körper (DE-588)4667267-9 gnd Kommutativer Ring (DE-588)4164825-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Assoziativer Ring (DE-588)4143228-9 gnd |
| topic_facet | Quadratischer Körper Kommutativer Ring Stochastischer Prozess Assoziativer Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014170866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
| work_keys_str_mv | AT polishchukalexander quadraticalgebras AT positselskileonid quadraticalgebras |