Two-dimensional conformal geometry and vertex operator algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1997
|
| Series: | Progress in mathematics
148 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 280 S. graph. Darst. |
| ISBN: | 0817638296 3764338296 |
Staff View
MARC
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| 100 | 1 | |a Huang, Yi-Zhi |d 1959- |e Verfasser |0 (DE-588)115554823 |4 aut | |
| 245 | 1 | 0 | |a Two-dimensional conformal geometry and vertex operator algebras |c Yi-Zhi Huang |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1997 | |
| 300 | |a XII, 280 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 148 | |
| 650 | 7 | |a Algèbres d'opérateurs des sommets |2 ram | |
| 650 | 7 | |a Conforme afbeelding |2 gtt | |
| 650 | 7 | |a Géométrie conforme |2 ram | |
| 650 | 7 | |a Operatoren |2 gtt | |
| 650 | 4 | |a Conformal geometry | |
| 650 | 4 | |a Vertex operator algebras | |
| 650 | 0 | 7 | |a Konforme Feldtheorie |0 (DE-588)4312574-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Konforme Differentialgeometrie |0 (DE-588)4206468-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dimension 2 |0 (DE-588)4321721-7 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Contents
Preface [x
Acknowledgments xi
Introduction 1
Notational conventions 16
Chapter 1. Spheres with tubes 17
1.1. Definitions 17
1.2. The sewing operation 19
1.3. The moduli spaces of spheres with tubes 22
1.4. The sewing equation 28
1.5. Meromorphic functions on the moduli spaces
and meromorphic tangent spaces 32
Chapter 2. Algebraic study of the sewing operation 35
2.1. Formal power series and exponentials of derivations 37
2.2. The formal sewing equation and the sewing identities 48
Chapter 3. Geometric study of the sewing operation 63
3.1. Moduli spaces, meromorphic functions
and meromorphic tangent spaces revisited 65
3.2. The sewing operation and spheres with tubes
oftype(l.O), (l,l)and(l,2) 69
3.3. Generalized spheres with tubes 74
3.4. The sewing formulas and the convergence
of the associated series via the Fischer Grauert Theorem 76
3.5. A Virasoro algebra structure of central charge 0
on the meromorphic tangent space of K(l) at its identity 88
Chapter 4. Realizations of the sewing identities 93
4.1. The Virasoro algebra and modules 94
4.2. Realizations of the sewing identities
for general representations of the Virasoro algebra 96
vi CONTENTS
4.3. Realizations of the sewing identities
for positive energy representations of the Virasoro algebra 102
Chapter 5. Geometric vertex operator algebras 109
5.1. Linear algebra of graded vector spaces
with finite dimensional homogeneous subspaces 109
5.2. The notion of geometric vertex operator algebra 111
5.3. Vertex operator algebras 113
5.4. The isomorphism between the category of geometric vertex
operator algebras and the category of vertex operator
algebras 119
Chapter 6. Vertex partial operads 143
6.1. The Cx rescalable partial operad structure
on the sequence K of moduli spaces 144
6.2. The topological and analytic structures on K 145
6.3. The associativity of the sphere partial operad K 147
6.4. Suboperads and partial suboperads of K 149
6.5. The determinant line bundles over K
and the partial operad structure 150
6.6. Meromorphic tangent spaces of determinant line bundles
and a module for the Virasoro algebra 158
6.7. Proof of the convergence of projective factors
in the sewing axiom 165
6.8. Complex powers of the determinant line bundles 167
6.9. C extensions of K 169
Chapter 7. The isomorphism theorem and applications 171
7.1. Vertex associative algebras 171
7.2. The isomorphism theorem 173
7.3. Geometric construction of some Virasoro
vertex operator algebras 175
7.4. Isomorphic vertex operator algebras
induced from conformal maps 176
Appendix A. Answers to selected exercises 185
A.I. Exercise 1.3.5: The proof of Proposition 1.3.4 185
A.2. Exercise 2.1.8: Another proof of Proposition 2.1.7 185
A.3. Exercise 2.1.12: The proof of Proposition 2.1.11 188
A.4. Exercise 2.1.17: The proof of Proposition 2.1.16 189
A.5. Exercise 2.1.20: The proof of Proposition 2.1.19 189
A.6. Exercise 3.4.2: The sewing formulas 189
A.7. Exercise 3.5.1: The definition of the Virasoro bracket 191
CONTENTS vii
A.8. Exercise 3.5.3: The calculation of the Virasoro bracket 192
A.9. Exercise 5.4.2: The proof of the permutation axiom
for a o n_i.n 196
A.10. Exercise 5.4.3: The proof of the formula (5.4.10) 197
A.11. Exercise 6.6.3: The proof of the formula (6.6.20) 198
A.12. Exercise 6.7.2: The proof of Lemma 6.7.1 199
Appendix B. (LB) spaces and complex (LB) manifolds 201
Appendix C. Operads and partial operads 205
C.I. Operads, partial operads and associated algebraic structures 205
C.2. Rescaling groups for partial operads, rescalable
partial operads and associated algebraic structures 209
C.3. Another definition of (partial) operad 213
Appendix D. Determinant lines and determinant line bundles 219
D.I. Some classes of bounded linear operators 220
D.2. Determinant lines 222
D.3. Determinant lines over Riemann surfaces
with parametrized boundaries 236
D.4. Canonical isomorphisms associated to sewing
and determinant line bundles over moduli spaces 240
D.5. The determinant line bundle and central extensions
of the difFeomorphism group of S1 255
D.6. One dimensional genus zero modular functors
and the Mumford Segal theorem 264
Bibliography 269
Index 275
|
| any_adam_object | 1 |
| author | Huang, Yi-Zhi 1959- |
| author_GND | (DE-588)115554823 |
| author_facet | Huang, Yi-Zhi 1959- |
| author_role | aut |
| author_sort | Huang, Yi-Zhi 1959- |
| author_variant | y z h yzh |
| building | Verbundindex |
| bvnumber | BV011506676 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA326 |
| callnumber-search | QA326 |
| callnumber-sort | QA 3326 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 280 SK 340 SK 600 |
| classification_tum | MAT 537f MAT 472f |
| ctrlnum | (OCoLC)35849139 (DE-599)BVBBV011506676 |
| dewey-full | 516.385 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.385 516.3/5 |
| dewey-search | 516.385 516.3/5 |
| dewey-sort | 3516.385 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:10:55Z |
| institution | BVB |
| isbn | 0817638296 3764338296 |
| language | English |
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| physical | XII, 280 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
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| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
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| spelling | Huang, Yi-Zhi 1959- Verfasser (DE-588)115554823 aut Two-dimensional conformal geometry and vertex operator algebras Yi-Zhi Huang Boston [u.a.] Birkhäuser 1997 XII, 280 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 148 Algèbres d'opérateurs des sommets ram Conforme afbeelding gtt Géométrie conforme ram Operatoren gtt Conformal geometry Vertex operator algebras Konforme Feldtheorie (DE-588)4312574-8 gnd rswk-swf Konforme Differentialgeometrie (DE-588)4206468-5 gnd rswk-swf Dimension 2 (DE-588)4321721-7 gnd rswk-swf Vertexalgebra (DE-588)4328736-0 gnd rswk-swf Vertexoperator (DE-588)4188067-5 gnd rswk-swf Vertexoperator (DE-588)4188067-5 s Vertexalgebra (DE-588)4328736-0 s Konforme Differentialgeometrie (DE-588)4206468-5 s Konforme Feldtheorie (DE-588)4312574-8 s Dimension 2 (DE-588)4321721-7 s DE-604 Progress in mathematics 148 (DE-604)BV000004120 148 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007743579&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Huang, Yi-Zhi 1959- Two-dimensional conformal geometry and vertex operator algebras Progress in mathematics Algèbres d'opérateurs des sommets ram Conforme afbeelding gtt Géométrie conforme ram Operatoren gtt Conformal geometry Vertex operator algebras Konforme Feldtheorie (DE-588)4312574-8 gnd Konforme Differentialgeometrie (DE-588)4206468-5 gnd Dimension 2 (DE-588)4321721-7 gnd Vertexalgebra (DE-588)4328736-0 gnd Vertexoperator (DE-588)4188067-5 gnd |
| subject_GND | (DE-588)4312574-8 (DE-588)4206468-5 (DE-588)4321721-7 (DE-588)4328736-0 (DE-588)4188067-5 |
| title | Two-dimensional conformal geometry and vertex operator algebras |
| title_auth | Two-dimensional conformal geometry and vertex operator algebras |
| title_exact_search | Two-dimensional conformal geometry and vertex operator algebras |
| title_full | Two-dimensional conformal geometry and vertex operator algebras Yi-Zhi Huang |
| title_fullStr | Two-dimensional conformal geometry and vertex operator algebras Yi-Zhi Huang |
| title_full_unstemmed | Two-dimensional conformal geometry and vertex operator algebras Yi-Zhi Huang |
| title_short | Two-dimensional conformal geometry and vertex operator algebras |
| title_sort | two dimensional conformal geometry and vertex operator algebras |
| topic | Algèbres d'opérateurs des sommets ram Conforme afbeelding gtt Géométrie conforme ram Operatoren gtt Conformal geometry Vertex operator algebras Konforme Feldtheorie (DE-588)4312574-8 gnd Konforme Differentialgeometrie (DE-588)4206468-5 gnd Dimension 2 (DE-588)4321721-7 gnd Vertexalgebra (DE-588)4328736-0 gnd Vertexoperator (DE-588)4188067-5 gnd |
| topic_facet | Algèbres d'opérateurs des sommets Conforme afbeelding Géométrie conforme Operatoren Conformal geometry Vertex operator algebras Konforme Feldtheorie Konforme Differentialgeometrie Dimension 2 Vertexalgebra Vertexoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007743579&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT huangyizhi twodimensionalconformalgeometryandvertexoperatoralgebras |