Introduction to vertex operator algebras and their representations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2004
|
| Series: | Progress in mathematics
227 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz.: S. [289] - 314 Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XI, 318 S. |
| ISBN: | 0817634088 3764334088 9780817634087 9781461264804 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to vertex operator algebras and their representations |c James Lepowsky ; Haisheng Li |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2004 | |
| 300 | |a XI, 318 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 227 | |
| 500 | |a Literaturverz.: S. [289] - 314 | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Vertex operator algebras | |
| 700 | 1 | |a Li, Haisheng |e Verfasser |0 (DE-588)1011251191 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-8176-8186-9 |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
1 Introduction 1
1.1 Motivation 1
1.2 Example of a vertex operator 5
1.3 The notion of vertex operator algebra 8
1.4 Simplification of the definition 12
1.5 Representations and modules 13
1.6 Construction of families of examples 15
1.7 Some further developments 17
2 Formal Calculus 21
2.1 Formal series and the formal delta function 21
2.2 Derivations and the formal Taylor Theorem 29
2.3 Expansions of zero and applications 33
3 Vertex Operator Algebras: The Axiomatic Basics 49
3.1 Definitions and some fundamental properties 49
3.2 Commutativity properties 65
3.3 Associativity properties 72
3.4 The Jacobi identity from commutativity and associativity 81
3.5 The Jacobi identity from commutativity 84
3.6 The Jacobi identity from skew symmetry and associativity 86
3.7 «S3 symmetry of the Jacobi identity 92
3.8 The iterate formula and normal ordered products 94
3.9 Further elementary notions 98
3.10 Weak nilpotence and nilpotence 101
3.11 Centralizers and the center 105
3.12 Direct product and tensor product vertex algebras Ill
viii Contents
4 Modules 117
4.1 Definition and some consequences 118
4.2 Commutativity properties 121
4.3 Associativity properties 124
4.4 The Jacobi identity as a consequence of associativity and
commutativity properties 127
4.5 Further elementary notions 128
4.6 Tensor product modules for tensor product vertex algebras 137
4.7 Vacuum like vectors 138
4.8 Adjoining a module to a vertex algebra 141
5 Representations of Vertex Algebras and the Construction of Vertex
Algebras and Modules 145
5.1 Weak vertex operators 148
5.2 The action of weak vertex operators on the space of weak vertex
operators 151
5.3 The canonical weak vertex algebra £(W) and the equivalence between
modules and representations 156
5.4 Subalgebras of £(W) 163
5.5 Local subalgebras and vertex subalgebras of £(W) 165
5.6 Vertex subalgebras of £(W) associated with the Virasoro algebra 173
5.7 General construction theorems for vertex algebras and modules 179
6 Construction of Families of Vertex Operator Algebras and Modules .... 191
6.1 Vertex operator algebras and modules associated to
the Virasoro algebra 193
6.2 Vertex operator algebras and modules associated to
affine Lie algebras 201
6.3 Vertex operator algebras and modules associated to
Heisenberg algebras 217
6.4 Vertex operator algebras and modules associated to
even lattices—the setting 226
6.5 Vertex operator algebras and modules associated to
even lattices—the main results 239
6.6 Classification of the irreducible Lg(£, 0) modules for g
finite dimensional simple and I a positive integer 264
References 289
Index 315
|
| adam_txt |
Contents
Preface ix
1 Introduction 1
1.1 Motivation 1
1.2 Example of a vertex operator 5
1.3 The notion of vertex operator algebra 8
1.4 Simplification of the definition 12
1.5 Representations and modules 13
1.6 Construction of families of examples 15
1.7 Some further developments 17
2 Formal Calculus 21
2.1 Formal series and the formal delta function 21
2.2 Derivations and the formal Taylor Theorem 29
2.3 Expansions of zero and applications 33
3 Vertex Operator Algebras: The Axiomatic Basics 49
3.1 Definitions and some fundamental properties 49
3.2 Commutativity properties 65
3.3 Associativity properties 72
3.4 The Jacobi identity from commutativity and associativity 81
3.5 The Jacobi identity from commutativity 84
3.6 The Jacobi identity from skew symmetry and associativity 86
3.7 «S3 symmetry of the Jacobi identity 92
3.8 The iterate formula and normal ordered products 94
3.9 Further elementary notions 98
3.10 Weak nilpotence and nilpotence 101
3.11 Centralizers and the center 105
3.12 Direct product and tensor product vertex algebras Ill
viii Contents
4 Modules 117
4.1 Definition and some consequences 118
4.2 Commutativity properties 121
4.3 Associativity properties 124
4.4 The Jacobi identity as a consequence of associativity and
commutativity properties 127
4.5 Further elementary notions 128
4.6 Tensor product modules for tensor product vertex algebras 137
4.7 Vacuum like vectors 138
4.8 Adjoining a module to a vertex algebra 141
5 Representations of Vertex Algebras and the Construction of Vertex
Algebras and Modules 145
5.1 Weak vertex operators 148
5.2 The action of weak vertex operators on the space of weak vertex
operators 151
5.3 The canonical weak vertex algebra £(W) and the equivalence between
modules and representations 156
5.4 Subalgebras of £(W) 163
5.5 Local subalgebras and vertex subalgebras of £(W) 165
5.6 Vertex subalgebras of £(W) associated with the Virasoro algebra 173
5.7 General construction theorems for vertex algebras and modules 179
6 Construction of Families of Vertex Operator Algebras and Modules . 191
6.1 Vertex operator algebras and modules associated to
the Virasoro algebra 193
6.2 Vertex operator algebras and modules associated to
affine Lie algebras 201
6.3 Vertex operator algebras and modules associated to
Heisenberg algebras 217
6.4 Vertex operator algebras and modules associated to
even lattices—the setting 226
6.5 Vertex operator algebras and modules associated to
even lattices—the main results 239
6.6 Classification of the irreducible Lg(£, 0) modules for g
finite dimensional simple and I a positive integer 264
References 289
Index 315 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:55:06Z |
| indexdate | 2024-07-09T20:35:18Z |
| institution | BVB |
| isbn | 0817634088 3764334088 9780817634087 9781461264804 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014628963 |
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| physical | XI, 318 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Lepowsky, James 1944- Verfasser (DE-588)134211766 aut Introduction to vertex operator algebras and their representations James Lepowsky ; Haisheng Li Boston [u.a.] Birkhäuser 2004 XI, 318 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 227 Literaturverz.: S. [289] - 314 Hier auch später erschienene, unveränderte Nachdrucke Vertex operator algebras Li, Haisheng Verfasser (DE-588)1011251191 aut Erscheint auch als Online-Ausgabe 978-0-8176-8186-9 Progress in mathematics 227 (DE-604)BV000004120 227 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014628963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lepowsky, James 1944- Li, Haisheng Introduction to vertex operator algebras and their representations Progress in mathematics Vertex operator algebras |
| title | Introduction to vertex operator algebras and their representations |
| title_auth | Introduction to vertex operator algebras and their representations |
| title_exact_search | Introduction to vertex operator algebras and their representations |
| title_exact_search_txtP | Introduction to vertex operator algebras and their representations |
| title_full | Introduction to vertex operator algebras and their representations James Lepowsky ; Haisheng Li |
| title_fullStr | Introduction to vertex operator algebras and their representations James Lepowsky ; Haisheng Li |
| title_full_unstemmed | Introduction to vertex operator algebras and their representations James Lepowsky ; Haisheng Li |
| title_short | Introduction to vertex operator algebras and their representations |
| title_sort | introduction to vertex operator algebras and their representations |
| topic | Vertex operator algebras |
| topic_facet | Vertex operator algebras |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014628963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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