Vertex algebras and algebraic curves:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2004]
|
| Edition: | Second edition |
| Series: | Mathematical surveys and monographs
volume 88 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 400 Seiten Diagramme |
| ISBN: | 0821836749 9780821836743 |
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Record in the Search Index
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| adam_text | Titel: Vertex algebras and algebraic curves
Autor: Frenkel, Edward
Jahr: 2004
Contents Preface to the Second Edition ix Preface to the First Edition xi Introduction 1 Chapter 1. Definition of Vertex Algebras 11 1.1. Formal distributions 11 1.2. Locality 16 1.3. Definition of a vertex algebra 20 1.4. First example: commutative vertex algebras 22 1.5. Bibliographical notes 23 Chapter 2. Vertex Algebras Associated to Lie Algebras 25 2.1. Heisenberg Lie algebra 25 2.2. The vertex algebra structure on 7r 28 2.3. Checking vertex algebra axioms 32 2.4. Affine Kac-Moody algebras and their vertex algebras 38 2.5. The Virasoro vertex algebra 42 2.6. Bibliographical notes 46 Chapter 3. Associativity and Operator Product Expansion 47 3.1. Goddard’s uniqueness theorem 47 3.2. Associativity 48 3.3. Operator product expansion 51 3.4. Examples of OPE 56 3.5. Bibliographical notes 61 Chapter 4. Applications of the Operator Product Expansion 63 4.1. A Lie algebra attached to a vertex algebra 63 4.2. U(V) and a completion of the universal enveloping algebra 65 4.3. An associative algebra attached to a vertex algebra 69 4.4. Strong reconstruction theorem 70 4.5. Correlation functions 72 4.6. Bibliographical notes 74 Chapter 5. Modules over Vertex Algebras and More Examples 75 5.1. Modules over vertex algebras 76 5.2. Vertex algebras associated to one-dimensional integral lattices 80 5.3. Boson-fermion correspondence 85 5.4. Lattice vertex algebras 88 V
CONTENTS vii® ÇÍMilpIpÇT IB-. Cidral Algebras 329 USIA Some sheaf theory 329 »J.. Sheaf interpretation of OPE 334 M?. CMral algebras 337 «1,4.. Lie* algebras 342 IM. Modules over chiral algebras 346 mx Global Kae-Moody and Virasoro algebras 34? mx Bibliograpiiical notes 350 Otel??’JT 2ft. Factorization. 351 m Firwriiatlut algebras 351 lAtftomiatfen algebras and chiral algebras 354 ÄS.. The Grassmannian and factorization spaces 358 2ft.4. feamptes of factorisation algebras 363 »A. IFactoÄatton and the chiral Hecke algebra 369 Äift. ÄMwigTíipMcial notes 374 Aupewrd? AX lifers, [formal! discs, and ind-schemes 37-5 375 AÃ. €kmmm:ikms 377 AA. ILiis- sslgclwõMs and D-modules 378 A4!.. IL» algebra. cohomology 380 läiMwpaipliy 383 393 39 í lîim m ?M aABte?itentlly W Notation
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| adam_txt |
Titel: Vertex algebras and algebraic curves
Autor: Frenkel, Edward
Jahr: 2004
Contents Preface to the Second Edition ix Preface to the First Edition xi Introduction 1 Chapter 1. Definition of Vertex Algebras 11 1.1. Formal distributions 11 1.2. Locality 16 1.3. Definition of a vertex algebra 20 1.4. First example: commutative vertex algebras 22 1.5. Bibliographical notes 23 Chapter 2. Vertex Algebras Associated to Lie Algebras 25 2.1. Heisenberg Lie algebra 25 2.2. The vertex algebra structure on 7r 28 2.3. Checking vertex algebra axioms 32 2.4. Affine Kac-Moody algebras and their vertex algebras 38 2.5. The Virasoro vertex algebra 42 2.6. Bibliographical notes 46 Chapter 3. Associativity and Operator Product Expansion 47 3.1. Goddard’s uniqueness theorem 47 3.2. Associativity 48 3.3. Operator product expansion 51 3.4. Examples of OPE 56 3.5. Bibliographical notes 61 Chapter 4. Applications of the Operator Product Expansion 63 4.1. A Lie algebra attached to a vertex algebra 63 4.2. U(V) and a completion of the universal enveloping algebra 65 4.3. An associative algebra attached to a vertex algebra 69 4.4. Strong reconstruction theorem 70 4.5. Correlation functions 72 4.6. Bibliographical notes 74 Chapter 5. Modules over Vertex Algebras and More Examples 75 5.1. Modules over vertex algebras 76 5.2. Vertex algebras associated to one-dimensional integral lattices 80 5.3. Boson-fermion correspondence 85 5.4. Lattice vertex algebras 88 V
CONTENTS vii® ÇÍMilpIpÇT IB-. Cidral Algebras 329 USIA Some sheaf theory 329 »J. Sheaf interpretation of OPE 334 M?. CMral algebras 337 «1,4. Lie* algebras 342 IM. Modules over chiral algebras 346 mx Global Kae-Moody and Virasoro algebras 34? mx Bibliograpiiical notes 350 Otel??’JT 2ft. Factorization. 351 m Firwriiatlut algebras 351 lAtftomiatfen algebras and chiral algebras 354 ÄS. The Grassmannian and factorization spaces 358 2ft.4. feamptes of factorisation algebras 363 »A. IFactoÄatton and the chiral Hecke algebra 369 Äift. ÄMwigTíipMcial notes 374 Aupewrd? AX lifers, [formal! discs, and ind-schemes 37-5 375 AÃ. €kmmm:ikms 377 AA. ILiis- sslgclwõMs and D-modules 378 A4!. IL»' algebra. cohomology 380 läiMwpaipliy 383 393 39 í lîim m ?M aABte?itentlly W Notation |
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| author | Frenkel, Edward 1968- Ben-Zvi, David 1974- |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Second edition |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:12:31Z |
| indexdate | 2024-07-09T21:09:07Z |
| institution | BVB |
| isbn | 0821836749 9780821836743 |
| language | English |
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| physical | xiii, 400 Seiten Diagramme |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | American Mathematical Society |
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| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Frenkel, Edward 1968- Verfasser (DE-588)173510116 aut Vertex algebras and algebraic curves Edward Frenkel ; David Ben-Zvi Second edition Providence, Rhode Island American Mathematical Society [2004] © 2004 xiii, 400 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs volume 88 Curves, Algebraic Vertex operator algebras Vertexalgebra (DE-588)4328736-0 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Vertexalgebra (DE-588)4328736-0 s Algebraische Kurve (DE-588)4001165-3 s DE-604 Ben-Zvi, David 1974- Verfasser (DE-588)173510124 aut Erscheint auch als Online-Ausgabe 978-1-4704-1315-6 Mathematical surveys and monographs volume 88 (DE-604)BV000018014 88 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016223673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frenkel, Edward 1968- Ben-Zvi, David 1974- Vertex algebras and algebraic curves Mathematical surveys and monographs Curves, Algebraic Vertex operator algebras Vertexalgebra (DE-588)4328736-0 gnd Algebraische Kurve (DE-588)4001165-3 gnd |
| subject_GND | (DE-588)4328736-0 (DE-588)4001165-3 |
| title | Vertex algebras and algebraic curves |
| title_auth | Vertex algebras and algebraic curves |
| title_exact_search | Vertex algebras and algebraic curves |
| title_exact_search_txtP | Vertex algebras and algebraic curves |
| title_full | Vertex algebras and algebraic curves Edward Frenkel ; David Ben-Zvi |
| title_fullStr | Vertex algebras and algebraic curves Edward Frenkel ; David Ben-Zvi |
| title_full_unstemmed | Vertex algebras and algebraic curves Edward Frenkel ; David Ben-Zvi |
| title_short | Vertex algebras and algebraic curves |
| title_sort | vertex algebras and algebraic curves |
| topic | Curves, Algebraic Vertex operator algebras Vertexalgebra (DE-588)4328736-0 gnd Algebraische Kurve (DE-588)4001165-3 gnd |
| topic_facet | Curves, Algebraic Vertex operator algebras Vertexalgebra Algebraische Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016223673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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