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| Frenkel E., Ben-Zvi D. — Vertex algebras and algebraic curves |
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| Предметный указатель |
algebra 320
-system 184
-differential 93
-structure 106
-connection 117
-modules 277 314 332
-algebra 231 300
-algebra, classical 270
Adjoint differential operator 125
Affine connection 117 199
Affine Kac-Moody algebras 38 96 105 130 136 211 249 256 324
Affine structure 118
Annihilation operator 28 192
Associativity 48
Atiyah sequence 130 332
bc-system 78
BGG resolution 244
Borcherds identity 56
Borel subalgebra 172 262
Boson-fermion correspondence 77
BRST complex 86 229 266 269
Cartan decomposition 172 178 199 228
Cartan subalgebra 172 228
Casimir tensor 214 294
Center of a vertex algebra 84 253 299
Central charge 42—44
Central extension 25 279 333
Central extension, universal 39
CHARACTER 79 82
Charge 227
Chevalley complex 147 334
Chiral algebra 156 309 317
Chiral correlation functions 157
Chiral de Rham complex 305
Chiral differential operators 306
Classical Drinfeld — Sokolov reduction 265
Coinvariants 135 150 277
Commutative vertex algebra 22
Configuration space 207
Conformal algebra 251 320
Conformal blocks 135 149
Conformal dimension 16
Conformal module 72
Conformal vector 44
Conformal vertex algebra 44
Connection 102 130 256 331
Contraction 193
Coset construction 84
Cousin property 49 162 319
Creation operator 28 192
Critical level 196 198 300
De Rham cohomology 138 222 321
Delta-function 12 312 320
Determinant line bundle 287
Disc 330
Disc, abstract 94
Disc, formal 89 329
Drinfeld — Sokolov reduction, quantum 229
Drinfeld—Sokolov reduction, classical 265
Dual Coxeter number 39
Enveloping vertex algebra 250
External tensor product 112 310
Fermionic Fock representation 77
Fiat bundle 222
Fiber of an -module 278
Field 16
Flag manifold 172 177
Flat connection 102 331
Flat structure 273 331
Fock representation 27 80 203
Formal coordinate 95 97
Formal disc 329
Formal distribution 11
Formal Laurent series 14
Formal power series 11
Formal scheme 329
Formal Taylor series 14
Free field realization 169 243
g-oper 263
Gauge transformations 128 129 257 262 265
Gauss — Manin connection 224
Geometric Langlands correspondence 246 304
Goddard — Kent — Olive construction 84
Hamiltonian reduction 265
Harish — Chandra pair 331
Heisenberg Lie algebra 26 128 134 135 164 203
Horizontal section 102
Ind-group 89 273 282 330
Ind-scheme 89 179 330
Infinitesimally nearby points 331
Invariant bilinear form 38
| Jacobi identity 317 320
Jacobi triple product identity 80
Jacobian variety 296
Jet scheme 144 179
Killing form 38 198 241
Kirillov — Kostant structure 256
Knizhnik — Zamolodchikov equations 203 214 215
Kodaira — Spencer isomorphism 284 292
Langlands dual group 199 303
Langlands dual Lie algebra 245 300
Lattice vertex algebra 80
Laurent polynomial 11
Level 39
Lie algebra 25
Lie algebra cohomology 26 175 192 334
Lie algebroid 276 332
Local coordinate 97
Local system 222
Locality 17
Loop algebra 38
Loop group 331
Loop space 180
Modular functor 150
Module over a vertex algebra 69
Moduli space of bundles 291
Moduli space of curves 280
Monster group 84
Moonshine Module 84
n-point functions 65 157
Normal ordering 31 53 184 192 323
Normalized bilinear form 39
Oper 261 265 300
Oper, 122 263
Operator product expansion (OPE) 49 51 313
Orbifold construction 83
PBW basis 27
Poincare — Birkhoff — Witt theorem 27
Poisson structure 256
Polydifferentials 164
Primary field 92
Projective connection 121 137 260
Projective structure 121
Pseudodifferential operators 123
Quantum Drinfeld — Sokolov reduction 229
Quantum group 158 223 244
Quasi-conformal vertex algebra 91
Rational vertex algebra 82 150
Reconstruction theorem 37 63
Representation, coinduced 173
Representation, induced 173 176 199 212
Residues 134 138 139 310
Restricted dual vector space 173
Schwarzian derivative 120
Screening operator 243
Semi-infinite cohomology 200 228 334
Shapiro’s Lemma 147 175 334
Singular vector 92 219
Stress-energy tensor 119
Sugawara construction 45 131
Sugawara vector 45 59 196 213 217
Theta characteristic 120 264
Theta line bundle 294 296
Torsor 94 106 107
Translation operator 20
Twist by a torsor 94
Twisted conformal blocks 146
Twisted differential operators (TDO) 175 279 333
Twisted module 83
Twisting property 107
Uniformization theorem 293
Universal enveloping algebra 27
Vacuum representation 39
Vacuum vector 20
Verma module 173 177 199
Verma module, contragredient 173 200 217
Vertex algebra 20
Vertex algebra bundle 98
Vertex algebra module 69
Vertex algebra, commutative 22
Vertex algebra, conformal 44
Vertex algebra, quasi-conformal 91
Vertex Lie algebra 247
Vertex operator 20
Vertex Poisson algebra 252 299
Virasoro algebra 41 120 137 249 260 324
W-algebra 231 300
W-algebra, classical 270
Wakimoto module 197 199
Wakimoto realization 196
Weyl algebra 27 165 171 175 176
Wick formula 193
Zariski topology 97
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