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catalog contributor b12204914.
catalog contributor b12204915.
catalog created "c2001.".
catalog date "2001".
catalog date "c2001.".
catalog dateCopyrighted "c2001.".
catalog description "18.4. Lie* algebras 320 -- 18.5. Factorization 323 -- 18.6. Global Kac-Moody and Virasoro algebras 324 -- A.1. Discs, formal discs and ind-schemes 329 -- A.2. Connections 331 -- A.3. Lie algebroids and D-modules 332 -- A.4. Lie algebra cohomology 334.".
catalog description "69 -- 4.2. Vertex algebras associated to one-dimensional integral lattices 72 -- 4.3. Boson-fermion correspondence 77 -- 4.4. Lattice vertex algebras 80 -- 4.5. Introducing rational vertex algebras 82 -- 4.6. Constructing new vertex algebras 83 -- Chapter 5. Vertex Algebra Bundles 87 -- 5.1. Group Aut O 87 -- 5.2. Exponentiating vector fields 89 -- 5.3. Primary fields 92 -- 5.4. Main construction 96 -- 5.5. A flat connection on the vertex algebra bundle 102 -- Chapter 6. Action of Internal Symmetries 105 -- 6.1. Affine algebras, revisited 105 -- 6.2. General twisting property 107 -- 6.3. Description of the n-point functions and modules 112 -- Chapter 7. Vertex Algebra Bundles: Examples 115 -- 7.1. Heisenberg algebra and affine connections 115 -- 7.2. Virasoro algebra and projective connections 119 -- 7.3. Pseudodifferential operators and kernels 123 -- 7.4.".
catalog description "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 -- Chapter 2. Vertex Algebras Associated to Lie Algebras 25 -- 2.1. Heisenberg Lie algebra 25 -- 2.2. Vertex algebra structure on [pi] 28 -- 2.3. Checking vertex algebra axioms 32 -- 2.4. Affine Kac-Moody algebras and their vertex algebras 38 -- 2.5. Virasoro vertex algebra 41 -- Chapter 3. Associativity and Operator Product Expansion 47 -- 3.1. Uniqueness theorem 47 -- 3.2. Associativity 48 -- 3.3. Operator product expansion 51 -- 3.4. Examples and applications of OPE 56 -- 3.5. A Lie algebra attached to a vertex algebra 60 -- 3.6. Strong Reconstruction Theorem 63 -- 3.7. Correlation functions 65 -- Chapter 4. Rational Vertex Algebras 69 -- 4.1. Modules over vertex algebras".
catalog description "Chapter 11. Free Field Realization II 185 -- 11.1. Weyl algebras in the infinite-dimensional case 185 -- 11.2. Local completion 190 -- 11.3. Wakimoto realization 196 -- Chapter 12. Knizhnik-Zamolodchikov Equations 203 -- 12.1. Conformal blocks in the Heisenberg case 203 -- 12.2. Moving the points 207 -- 12.3. Conformal blocks for affine Kac-Moody algebras 211 -- Chapter 13. Solving the KZ Equations 215 -- 13.1. Conformal blocks from the point of view of free field realization 215 -- 13.2. Generalization: singular vectors 219 -- 13.3. Finding solutions 222 -- Chapter 14. Quantum Drinfeld-Sokolov Reduction and W-algebras 227 -- 14.1. BRST complex 227 -- 14.2. Proof of the main theorem 231 -- 14.4. Second computation 237 -- Chapter 15. Vertex Lie Algebras and Classical Limits 247 -- 15.1. Vertex Lie algebras 247 -- 15.2. Vertex Poisson algebras 252 -- 15.3.".
catalog description "Gauge action on the Heisenberg bundle 128 -- 7.5. Affine Kac-Moody vertex algebras and connections 130 -- Chapter 8. Conformal Blocks I 133 -- 8.1. Defining conformal blocks for the Heisenberg algebra 133 -- 8.2. Definition of conformal blocks for general vertex algebras 136 -- 8.3. Comparison of the two definitions of conformal blocks 140 -- 8.4. Coinvariants for commutative vertex algebras 143 -- 8.5. Twisted version of conformal blocks 145 -- 8.6. Appendix. Proof of Proposition 8.3.2 146 -- Chapter 9. Conformal Blocks II 149 -- 9.1. Multiple points 149 -- 9.2. Functoriality of conformal blocks 151 -- 9.3. Chiral correlation functions 153 -- 9.4. Conformal blocks in genus zero 158 -- 9.5. Functional realization of Heisenberg conformal blocks 164 -- Chapter 10. Free Field Realization I 169 -- 10.2. Finite-dimensional setting 171 -- 10.3. Infinite-dimensional setting 177 --".
catalog description "Includes bibliographical references (p. 335-342) and index.".
catalog description "Kac-Moody and Virasoro limits 254 -- 15.4. Poisson structure on connections 256 -- 15.5. Virasoro Poisson structure 260 -- 15.6. Opers 261 -- 15.7. Classical Drinfeld-Sokolov reduction 265 -- 15.8. Comparison of the classical and quantumC Drinfeld-Sokolov reductions 268 -- Chapter 16. Vertex Algebras and Moduli Spaces I 271 -- 16.1. Flat connection on the vertex algebra bundle, revisited 272 -- 16.2. Harish-Chandra pairs 275 -- 16.3. Moduli of curves 280 -- Chapter 17. Vertex Algebras and Moduli Spaces II 291 -- 17.1. Moduli of bundles 291 -- 17.2 Local structure of moduli spaces 297 -- 17.3. Global structure of moduli spaces 298 -- 17.4. Localization for affine algebras at the critical level 299 -- 17.5. Chiral de Rham complex 304 -- Chapter 18. Chiral Algebras 309 -- 18.1. Some sheaf theory 309 -- 18.2. Sheaf interpretation of OPE 313 -- 18.3. Chiral algebras 316 --".
catalog extent "xii, 348 p. :".
catalog hasFormat "Vertex algebras and algebraic curves.".
catalog identifier "0821828940 (acid-free paper)".
catalog isFormatOf "Vertex algebras and algebraic curves.".
catalog isPartOf "Mathematical surveys and monographs ; no. 88.".
catalog isPartOf "Mathematical surveys and monographs, 0076-5376 ; v. 88".
catalog issued "2001".
catalog issued "c2001.".
catalog language "eng".
catalog publisher "Providence, R.I. : American Mathematical Society,".
catalog relation "Vertex algebras and algebraic curves.".
catalog subject "512/.55 21".
catalog subject "Curves, Algebraic.".
catalog subject "QA326 .F76 2001".
catalog subject "Vertex operator algebras.".
catalog tableOfContents "18.4. Lie* algebras 320 -- 18.5. Factorization 323 -- 18.6. Global Kac-Moody and Virasoro algebras 324 -- A.1. Discs, formal discs and ind-schemes 329 -- A.2. Connections 331 -- A.3. Lie algebroids and D-modules 332 -- A.4. Lie algebra cohomology 334.".
catalog tableOfContents "69 -- 4.2. Vertex algebras associated to one-dimensional integral lattices 72 -- 4.3. Boson-fermion correspondence 77 -- 4.4. Lattice vertex algebras 80 -- 4.5. Introducing rational vertex algebras 82 -- 4.6. Constructing new vertex algebras 83 -- Chapter 5. Vertex Algebra Bundles 87 -- 5.1. Group Aut O 87 -- 5.2. Exponentiating vector fields 89 -- 5.3. Primary fields 92 -- 5.4. Main construction 96 -- 5.5. A flat connection on the vertex algebra bundle 102 -- Chapter 6. Action of Internal Symmetries 105 -- 6.1. Affine algebras, revisited 105 -- 6.2. General twisting property 107 -- 6.3. Description of the n-point functions and modules 112 -- Chapter 7. Vertex Algebra Bundles: Examples 115 -- 7.1. Heisenberg algebra and affine connections 115 -- 7.2. Virasoro algebra and projective connections 119 -- 7.3. Pseudodifferential operators and kernels 123 -- 7.4.".
catalog tableOfContents "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 -- Chapter 2. Vertex Algebras Associated to Lie Algebras 25 -- 2.1. Heisenberg Lie algebra 25 -- 2.2. Vertex algebra structure on [pi] 28 -- 2.3. Checking vertex algebra axioms 32 -- 2.4. Affine Kac-Moody algebras and their vertex algebras 38 -- 2.5. Virasoro vertex algebra 41 -- Chapter 3. Associativity and Operator Product Expansion 47 -- 3.1. Uniqueness theorem 47 -- 3.2. Associativity 48 -- 3.3. Operator product expansion 51 -- 3.4. Examples and applications of OPE 56 -- 3.5. A Lie algebra attached to a vertex algebra 60 -- 3.6. Strong Reconstruction Theorem 63 -- 3.7. Correlation functions 65 -- Chapter 4. Rational Vertex Algebras 69 -- 4.1. Modules over vertex algebras".
catalog tableOfContents "Chapter 11. Free Field Realization II 185 -- 11.1. Weyl algebras in the infinite-dimensional case 185 -- 11.2. Local completion 190 -- 11.3. Wakimoto realization 196 -- Chapter 12. Knizhnik-Zamolodchikov Equations 203 -- 12.1. Conformal blocks in the Heisenberg case 203 -- 12.2. Moving the points 207 -- 12.3. Conformal blocks for affine Kac-Moody algebras 211 -- Chapter 13. Solving the KZ Equations 215 -- 13.1. Conformal blocks from the point of view of free field realization 215 -- 13.2. Generalization: singular vectors 219 -- 13.3. Finding solutions 222 -- Chapter 14. Quantum Drinfeld-Sokolov Reduction and W-algebras 227 -- 14.1. BRST complex 227 -- 14.2. Proof of the main theorem 231 -- 14.4. Second computation 237 -- Chapter 15. Vertex Lie Algebras and Classical Limits 247 -- 15.1. Vertex Lie algebras 247 -- 15.2. Vertex Poisson algebras 252 -- 15.3.".
catalog tableOfContents "Gauge action on the Heisenberg bundle 128 -- 7.5. Affine Kac-Moody vertex algebras and connections 130 -- Chapter 8. Conformal Blocks I 133 -- 8.1. Defining conformal blocks for the Heisenberg algebra 133 -- 8.2. Definition of conformal blocks for general vertex algebras 136 -- 8.3. Comparison of the two definitions of conformal blocks 140 -- 8.4. Coinvariants for commutative vertex algebras 143 -- 8.5. Twisted version of conformal blocks 145 -- 8.6. Appendix. Proof of Proposition 8.3.2 146 -- Chapter 9. Conformal Blocks II 149 -- 9.1. Multiple points 149 -- 9.2. Functoriality of conformal blocks 151 -- 9.3. Chiral correlation functions 153 -- 9.4. Conformal blocks in genus zero 158 -- 9.5. Functional realization of Heisenberg conformal blocks 164 -- Chapter 10. Free Field Realization I 169 -- 10.2. Finite-dimensional setting 171 -- 10.3. Infinite-dimensional setting 177 --".
catalog tableOfContents "Kac-Moody and Virasoro limits 254 -- 15.4. Poisson structure on connections 256 -- 15.5. Virasoro Poisson structure 260 -- 15.6. Opers 261 -- 15.7. Classical Drinfeld-Sokolov reduction 265 -- 15.8. Comparison of the classical and quantumC Drinfeld-Sokolov reductions 268 -- Chapter 16. Vertex Algebras and Moduli Spaces I 271 -- 16.1. Flat connection on the vertex algebra bundle, revisited 272 -- 16.2. Harish-Chandra pairs 275 -- 16.3. Moduli of curves 280 -- Chapter 17. Vertex Algebras and Moduli Spaces II 291 -- 17.1. Moduli of bundles 291 -- 17.2 Local structure of moduli spaces 297 -- 17.3. Global structure of moduli spaces 298 -- 17.4. Localization for affine algebras at the critical level 299 -- 17.5. Chiral de Rham complex 304 -- Chapter 18. Chiral Algebras 309 -- 18.1. Some sheaf theory 309 -- 18.2. Sheaf interpretation of OPE 313 -- 18.3. Chiral algebras 316 --".
catalog title "Vertex algebras and algebraic curves / Edward Frenkel, David Ben-Zvi.".
catalog type "text".