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| Ïîèñê ïî óêàçàòåëÿì |
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| Chari V., Pressley A. — A Guide to Quantum Groups |
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| Ïðåäìåòíûé óêàçàòåëü |
*-homomorphism 117
*-representation 433 437—439 441—442
3-manifold invariants 522—525
Absolute Galois group 557—560
Admissible 80 92 482
Affiliated element 462
Affine Hecke algebra 403
Affine Hecke algebra, relation with p-adic groups 404
Affine Hecke algebra, representations 405—408 410—413
Affine Lie algebra 58 541—543 550—556 565—566
Alexander polynomial 498 500
Algebra 101—102
Algebra, deformation 43
Algebra, opposite 101
Ambient isotopy 496 514
Angle 1-form 501
Antipode 103 529
Antipode, square of 190—192
arrow 482
Associativity constraint 139
Baker — Campbell — Hausdorff formula 46 182 185—186
Big cell 294
Birkhoff factorization theorem 96
Birman — Murakami — Wenzl algebra 334 526
Boltzmann weight 247 351 510
BOND 246
Braid 142—144
Braid closure 501
Braid group 143—144 153 256
Braid group and configuration spaces 538
Braid group, action 257 282 336
Brauer — Frobenius — Schur duality see Frobenius — Schur duality
Bruhat decomposition 39 41
Bruhat ordering 360 405 565
Burau representation 505
C* -completion 451—452
C* -completion, type of 454
Capelli identity 426
Cartan matrix 562
Cartan matrix, extended 565—566
Casimir element 196 275—276
Category, abelian 136—137 307
Category, additive 136—137
Category, balanced 154
Category, braided monoidal 153
Category, essentially small 148
Category, k-linear 137
Category, monoidal 138—147 530
Category, quasitensor 152—153 329 359 370 531 555 559—560
Category, rigid 139—140 530 555
Category, semisimple 137 391 556
Category, small 148
Category, strict 139
Category, tensor 149—152 531
Central character 290 315 340
Central elements 122 124 168—169 284 321—323
CHARACTER 317 325—326 353—354 361 363
Characteristic p 296 304—306 358—361 555—556
Classical limit of a QF algebra 179
Classical limit of a quasi-Hopf QUE algebra 536—537
Classical limit of a QUE algebra 180—182
Classical r-matrix 54 181—182 183—184
Classical r-matrix and 2-cocycles 62—63
Classical r-matrix and integrable systems 71—77
Classical r-matrix, non-degenerate 62 87
Classical Yang — Baxter equation (CYBE) 54 125 182 187
Classical Yang — Baxter equation (CYBE) and Lie bialgebras 51
Classical Yang — Baxter equation (CYBE) with spectral parameters 87
Classical Yang — Baxter equation (CYBE), class of solution of 96
Classical Yang — Baxter equation (CYBE), equivalent solutions of 80 84 88
Classical Yang — Baxter equation (CYBE), modified 55
Classical Yang — Baxter equation (CYBE), solutions of 80—98
Clebsch — Gordan decomposition 204 326
Co-Jacobi identity 178
Co-Leibniz identity 178
Co-Poisson algebra 178
Co-Poisson Hopf algebra 178
Coadjoint orbits 20 40—41
Coalgebra 102—103
Coassociativity 102
Coassociator 529
Coboundary 51 84 174
Cochain 173
Cocommutator 25 535
Cocycle 25 62 174 533
Cohomology of Hopf algebras 173—177
Cohomology of Hopf algebras, rigidity theorems for 176—177 212
Cokernel 137
Comodule 108
Comodule algebra 109
Comodule coalgebra 109
Compact matrix pseudogroup see compact matrix quantum group
Compact matrix quantum group 453—454
Compact matrix quantum group, Haar integral 454—458
Complete integrability 68—69
Complete reducibility 318—319 324—325
Comultiplication 102
Configuration spaces 537—538 558
Conformal field theory 159 371—372
Conformal field theory, orbifold 534
Conformal weight 542
Conserved quantities 69
Conserved quantities in involution 69
Continued fraction 331
Continuous series 331
Contravariant form 320
Convolution product 104
Core 146
Corepresentation 110 141
Corepresentation, regular 110
Corepresentation, unitary 118
Coxeter automorphism 91
Coxeter element 489 565
Coxeter number 92 489 565
Crystal basis 478—486
Crystal basis, global 480—486
Crystal graph 484
De Rham complex of quantum  244—245
De Rham complex of quantum  matrices 242—243
De Rham complex of quantum plane 240—241
De Rham complex, homology of 243—244
Deformation of algebras 43
Deformation of bialgebras 171
Deformation of Hopf algebras 171
Deformation of Poisson algebras 44
Deformation, (mod  ) 172
Deformation, quantization 44 46—47
Degenerate affine Hecke algebra 405
Derivation 190—192
Determinant formula 321 327
Diagonal module 342
Diagram automorphism 309
Differential graded algebra 242
Direct sum 136
Directed tangle 145
Discrete series 330
Discriminant 340—341
Dressing action 37—38
Dressing action and symplectic leaves 38—41
Dressing transformation 37—38
Dual basis lemma 141
Dual Coxeter number 564
Dual object 139
Dual object functor 140
Dynkin diagram 92 562
Dynkin graph 307
Eight vertex model 253
Elliptic solutions of the CYBE 90—91
Elliptic solutions of the QYBE 427
Enhanced quantum Yang — Baxter operator 506
| Epimorphism 137
Equivalence of deformations 171
Equivalence of solutions of the CYBE 80 84 8?
Euclidean group 459
Evaluation homomorphism for affine Hecke algebras 407
Evaluation homomorphism for quantum loop algebras 399—401
Evaluation homomorphism for Yangians 386—387
Evaluation representations of affine Hecke algebras 407
Evaluation representations of quantum loop algebras 399—403
Evaluation representations of Yangians 386—391
Exterior algebra 107—108
Fateev — Zamolodchikov model 351
Fibonacci sequence 331
Framing 502
Frobenius Lie algebra 84
Frobenius map 305—306 357 359
Frobenius — Schur duality for  334—335 408—410
Frobenius — Schur duality for quantum affine algebras 410—413
Frobenius — Schur duality for Yangians 413—414
Frobenius — Schur duality, classical 332
Fuchsian differential equations 544
Functor, exact 148
Functor, faithful 148
Functor, monoidal 138—139
Functor, tensor 150
Fundamental reflection see simple reflection
Fundamental representations of quantum loop algebras 399
Fundamental representations of Yangians 384 387—388
Fundamental weight 564
Fusion matrices 155
Fusion ring 155 159 160 371
Fusion rules 154—157 160
Fusion tensor product 371 552—555
Gabriel's theorem 307—308 489
Gel'fand — Naimark — Segal state 439
Gel'fand — Tsetlin basis 476—478
Generalized Cartan matrix 562
Graphs, admissible 482
Graphs, coloured oriented 482
Graphs, crystal 484
Graphs, tensor products of 483—486
Grothendieck group 137—138
Grothendieck ring 139 156
Grothendieck — Teichmuller group 558—559
Grothendieck — Teichmuller group and quasi-Hopf algebras 559—560
Group algebra 105 112 175
Group cohomology 533—534
Group-like 106 193
H-adic topology 105
Haar integral see integral invariant
Hamiltonian 68—69
Hamiltonian vector field 17
Harish Chandra homomorphism 284 290 321—324
Harish Chandra homomorphism and quantum coadjoint action 296
Harish Chandra's theorem 285 290
Hecke algebra 332—336 404 476
Hecke algebra, representations 405—406
Heisenberg ferromagnet see XXX model
Heisenberg group 45 218
Heisenberg Lie algebra 44—45 176 186
Hermitian symmetric space 41
Highest weight 314 354 383 434 441
Highest weight module 314 324 354 542
Highest weight module for QF algebras 434 441
Highest weight module for Yangians 383
Highest weight vector 314 383
Hilbert space tensor product 415
Hochschild cohomology 174 254
Homfly polynomial 497—498 509 517
HOMFLY polynomial for trefoil knot 498—499
Hopf algebra 103—105
Hopf algebra, *-structure 117—119 309—311 329 431—432
Hopf algebra, almost cocommutative 119
Hopf algebra, coboundary 123
Hopf algebra, cocommutative 102
Hopf algebra, cohomology 173—177
Hopf algebra, deformations 171
Hopf algebra, dual 111—115 131—132 223—226 234—235
Hopf algebra, Graded 105
Hopf algebra, integral on 115—116 132
Hopf algebra, quasitriangular 123 129—130
Hopf algebra, representations 108—112
Hopf algebra, ribbon 125 133
Hopf algebra, topological 105 114 123
Hopf algebra, triangular 123 150—151
Hopf ideal 103—104
Hopf link 165—166
Hopf's theorem 108
Hyperalgebra 304 358 359—360
Identity object 138
Infinite-dimensional orthogonal group 414—417
Infinitesimal deformation 172
integral 115—116
Integral form, non-restricted 289
Integral form, restricted 297
Intersection cohomology 489
Intertwiner 151 348—351 542
Invariant 115
Invariant bilinear form 563
Invariant bilinear form, orthogonality properties 564
Invariant differential form 245—246
Invariant, non-central 456
Invariant, normalized 115
Ising model 371—372
Jackson integral 457 467
Jacobi identity 17
Jacobson topology 454
Jets 391
Jones polynomial 168 498 500
Kac — Moody algebra 562
Kashiwara's tensor product algorithm 485—486
Kauffman polynomial 499 500 510 517
Kazhdan — Lusztig element 406
Kazhdan — Lusztig polynomial 360
Kazhdan — Lusztig tensor product 552—555
Kernel 137
Kink 501
Kirby move 503 522—525
Kirby move, special 503
Kirillov — Kostant principle see orbit principle
Knizhnik — Zamolodchikov equation 539—541
Knizhnik — Zamolodchikov equation and hyperplane complements 561
Knizhnik — Zamolodchikov equation and m-point functions 542—543
Knizhnik — Zamolodchikov equation and quantization 543—549 555
Knot 496
Kohno — Drinfel'd monodromy theorem 549—550
Lattice model, exactly solvable 247
Lattice model, integrable 246—253
Lax pair 69—71 73 76
Left dual 111 122
Leibniz identity 17
Length 565
Level 408—409
Level for affine Lie algebras 566
Lie bialgebra 24—33
Lie bialgebra, automorphism 32
Lie bialgebra, coboundary 50—59
Lie bialgebra, cocommutator of 25
Lie bialgebra, derivation 32—33
Lie bialgebra, double 34—35 58—59
Lie bialgebra, dual 33—34
Lie bialgebra, factorizable 67
Lie bialgebra, homomorphism 25
Lie bialgebra, ideal 25
Lie bialgebra, opposite 25
Lie bialgebra, pseudotriangular 56
Lie bialgebra, quasitriangular 54
Lie bialgebra, quotient 25
Lie bialgebra, standard 29—30 34—36 55—56 59 81 93
Lie bialgebra, tangent 26
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