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Vertex algebras and algebraic curves /

Frenkel, Edward, (1968-)

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Vertex algebras and algebraic curves /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Vertex algebras and algebraic curves // Edward Frenkel, David Ben-Zvi.
Author:	Frenkel, Edward,
other author:	Ben-Zvi, David,
Published:	Providence, R.I. :American Mathematical Society, : c2001.,
Description:	xii, 348 p. ;27 cm.
Subject:	Vertex operator algebras. -
ISBN:	0821828940 (hbk.) :

Vertex algebras and algebraic curves /
Frenkel, Edward,1968-

Vertex algebras and algebraic curves /Edward Frenkel, David Ben-Zvi. - Providence, R.I. :American Mathematical Society,c2001. - xii, 348 p. ;27 cm. - Mathematical surveys and monographs,v. 880076-5376 ;. - Mathematical surveys and monographs ;no. 166..

Includes bibliographical references (p. 335-342) and index.

Definition of Vertex AlgebrasChapter 1.

ISBN: 0821828940 (hbk.) :US55.00

LCCN: 2001032794Subjects--Topical Terms:

532604
Vertex operator algebras.

LC Class. No.: QA326 / .F76 2001

Dewey Class. No.: 512/.55

Vertex algebras and algebraic curves /
LDR:06072cam a2200325 a 4500 001 980813
003 OCoLC
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008 111115s2001 nyua b 001 0 eng d
010 $a 2001032794
020 $a 0821828940 (hbk.) : $c US55.00
020 $a 9780821828946 (hbk.)
029 1 $a NLGGC $b 228685621
029 1 $a YDXCP $b 1783297
029 1 $a NZ1 $b 6267934
029 1 $a AU@ $b 000022673679
029 1 $a HEBIS $b 100138950
035 $a (OCoLC)46872350
035 $a AS-BW-100-08
040 $a DLC $c DLC $d NLGGC $d BTCTA $d YDXCP $d BAKER $d OCLCG $d VA@
042 $a pcc
049 $a FISA
050 0 0 $a QA326 $b .F76 2001
082 0 0 $a 512/.55 $2 21
100 1 $a Frenkel, Edward, $d 1968- $3 779037
245 1 0 $a Vertex algebras and algebraic curves / $c Edward Frenkel, David Ben-Zvi.
260 # $a Providence, R.I. : $b American Mathematical Society, $c c2001.
300 $a xii, 348 p. ; $c 27 cm.
490 1 $a Mathematical surveys and monographs, $x 0076-5376 ; $v v. 88
504 $a Includes bibliographical references (p. 335-342) and index.
505 0 0 $g Chapter 1. $t Definition of Vertex Algebras $g 11 -- $g 1.1. $t Formal distributions $g 11 -- $g 1.2. $t Locality $g 16 -- $g 1.3. $t Definition of a vertex algebra $g 20 -- $g 1.4. $t First example: commutative vertex algebras $g 22 -- $g Chapter 2. $t Vertex Algebras Associated to Lie Algebras $g 25 -- $g 2.1. $t Heisenberg Lie algebra $g 25 -- $g 2.2. $t Vertex algebra structure on [pi] $g 28 -- $g 2.3. $t Checking vertex algebra axioms $g 32 -- $g 2.4. $t Affine Kac-Moody algebras and their vertex algebras $g 38 -- $g 2.5. $t Virasoro vertex algebra $g 41 -- $g Chapter 3. $t Associativity and Operator Product Expansion $g 47 -- $g 3.1. $t Uniqueness theorem $g 47 -- $g 3.2. $t Associativity $g 48 -- $g 3.3. $t Operator product expansion $g 51 -- $g 3.4. $t Examples and applications of OPE $g 56 -- $g 3.5. $t A Lie algebra attached to a vertex algebra $g 60 -- $g 3.6. $t Strong Reconstruction Theorem $g 63 -- $g 3.7. $t Correlation functions $g 65 -- $g Chapter 4. $t Rational Vertex Algebras $g 69 -- $g 4.1. $t Modules over vertex algebras $g 69 -- $g 4.2. $t Vertex algebras associated to one-dimensional integral lattices $g 72 -- $g 4.3. $t Boson-fermion correspondence $g 77 -- $g 4.4. $t Lattice vertex algebras $g 80 -- $g 4.5. $t Introducing rational vertex algebras $g 82 -- $g 4.6. $t Constructing new vertex algebras $g 83 -- $g Chapter 5. $t Vertex Algebra Bundles $g 87 -- $g 5.1. $t Group Aut O $g 87 -- $g 5.2. $t Exponentiating vector fields $g 89 -- $g 5.3. $t Primary fields $g 92 -- $g 5.4. $t Main construction $g 96 -- $g 5.5. $t A flat connection on the vertex algebra bundle $g 102 -- $g Chapter 6. $t Action of Internal Symmetries $g 105 -- $g 6.1. $t Affine algebras, revisited $g 105 -- $g 6.2. $t General twisting property $g 107 -- $g 6.3. $t Description of the n-point functions and modules $g 112 -- $g Chapter 7. $t Vertex Algebra Bundles: Examples $g 115 -- $g 7.1. $t Heisenberg algebra and affine connections $g 115 -- $g 7.2. $t Virasoro algebra and projective connections $g 119 -- $g 7.3. $t Pseudodifferential operators and kernels $g 123 -- $g 7.4. $t Gauge action on the Heisenberg bundle $g 128 -- $g 7.5. $t Affine Kac-Moody vertex algebras and connections $g 130 -- $g Chapter 8. $t Conformal Blocks I $g 133 -- $g 8.1. $t Defining conformal blocks for the Heisenberg algebra $g 133 -- $g 8.2. $t Definition of conformal blocks for general vertex algebras $g 136 -- $g 8.3. $t Comparison of the two definitions of conformal blocks $g 140 -- $g 8.4. $t Coinvariants for commutative vertex algebras $g 143 -- $g 8.5. $t Twisted version of conformal blocks $g 145 -- $g 8.6. $t Appendix. Proof of Proposition 8.3.2 $g 146 -- $g Chapter 9. $t Conformal Blocks II $g 149 -- $g 9.1. $t Multiple points $g 149 -- $g 9.2. $t Functoriality of conformal blocks $g 151 -- $g 9.3. $t Chiral correlation functions $g 153 -- $g 9.4. $t Conformal blocks in genus zero $g 158 -- $g 9.5. $t Functional realization of Heisenberg conformal blocks $g 164 -- $g Chapter 10. $t Free Field Realization I $g 169 -- $g 10.2. $t Finite-dimensional setting $g 171 -- $g 10.3. $t Infinite-dimensional setting $g 177 -- $g Chapter 11. $t Free Field Realization II $g 185 -- $g 11.1. $t Weyl algebras in the infinite-dimensional case $g 185 -- $g 11.2. $t Local completion $g 190 -- $g 11.3. $t Wakimoto realization $g 196 -- $g Chapter 12. $t Knizhnik-Zamolodchikov Equations $g 203 -- $g 12.1. $t Conformal blocks in the Heisenberg case $g 203 -- $g 12.2. $t Moving the points $g 207 -- $g 12.3. $t Conformal blocks for affine Kac-Moody algebras $g 211 -- $g Chapter 13. $t Solving the KZ Equations $g 215 -- $g 13.1. $t Conformal blocks from the point of view of free field realization $g 215 -- $g 13.2. $t Generalization: singular vectors $g 219 -- $g 13.3. $t Finding solutions $g 222 -- $g Chapter 14. $t Quantum Drinfeld-Sokolov Reduction and W-algebras $g 227 -- $g 14.1. $t BRST complex $g 227 -- $g 14.2. $t Proof of the main theorem $g 231 -- $g 14.4. $t Second computation $g 237 -- $g Chapter 15. $t Vertex Lie Algebras and Classical Limits $g 247 -- $g 15.1. $t Vertex Lie algebras $g 247 -- $g 15.2. $t Vertex Poisson algebras $g 252 -- $g 15.3. $t Kac-Moody and Virasoro limits $g 254 -- $g 15.4. $t Poisson structure on connections $g 256 -- $g 15.5. $t Virasoro Poisson structure $g 260 -- $g 15.6. $t Opers $g 261 -- $g 15.7. $t Classical Drinfeld-Sokolov reduction $g 265 -- $g 15.8. $t Comparison of the classical and quantumC Drinfeld-Sokolov reductions $g 268 -- $g Chapter 16. $t Vertex Algebras and Moduli Spaces I $g 271 -- $g 16.1. $t Flat connection on the vertex algebra bundle, revisited $g 272 -- $g 16.2. $t Harish-Chandra pairs $g 275 -- $g 16.3. $t Moduli of curves $g 280 -- $g Chapter 17. $t Vertex Algebras and Moduli Spaces II $g 291 -- $g 17.1. $t Moduli of bundles $g 291 -- $g 17.2 $t Local structure of moduli spaces $g 297 -- $g 17.3. $t Global structure of moduli spaces $g 298 -- $g 17.4. $t Localization for affine algebras at the critical level $g 299 -- $g 17.5. $t Chiral de Rham complex $g 304 -- $g Chapter 18. $t Chiral Algebras $g 309 -- $g 18.1. $t Some sheaf theory $g 309 -- $g 18.2. $t Sheaf interpretation of OPE $g 313 -- $g 18.3. $t Chiral algebras $g 316 -- $g 18.4. $t Lie* algebras $g 320 -- $g 18.5. $t Factorization $g 323 -- $g 18.6. $t Global Kac-Moody and Virasoro algebras $g 324 -- $g A.1. $t Discs, formal discs and ind-schemes $g 329 -- $g A.2. $t Connections $g 331 -- $g A.3. $t Lie algebroids and D-modules $g 332 -- $g A.4. $t Lie algebra cohomology $g 334.
650 # 0 $a Vertex operator algebras. $3 532604
650 # 0 $a Curves, Algebraic. $3 540522
700 1 # $a Ben-Zvi, David, $d 1974- $3 779036
776 0 8 $i Online version: $a Frenkel, Edward, 1968- $t Vertex algebras and algebraic curves. $d Providence, R.I. : American Mathematical Society, c2001 $w (OCoLC)623809179
830 0 $a Mathematical surveys and monographs ; $v no. 166. $3 1236025