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| Majid S. — Foundations of Quantum Group Theory |
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| Предметный указатель |
Fredholm module 434
Free algebra 4 119 543
Free braided group 543
functor 15 276—278 417—426 476
Functor, contravariant 417 459
Functor, equivalence 418
Functor, forgetful 419 421 491
Functor, monoidal 421 426 468—471 478 486
Functor, multiplicative 474 496
Functor, representable 460 470
Functorial 418—420 439 460 512 527
Fundamental corepresentation 437 458
Fundamental operator 30—33 244
Galois theory 257—259
Gelfand — Naimark — Segal construction 32 195 205 212
Generic q 92 325 343 436 454 551
Grading 20 24 115 179 210 294 433 494 510
Grassmann variable 500—502 557
Gravity xiv 213 270—272 277 283
Group 1
Group algebra 12—15 45 50 189 266 294 416 481
Group convolution algebra 13
Group function algebra 12—15 20 45 54 125 188 225
Group grading See Grading
Group-like element 13 53
Haar weight 28 33
Half-real form 362 386 411
Hamiltonian 72 196 217 272 348 401 404 409 456
Hecke 124 152 163 166 514 551 559 564 570 579
Hecke algebra 467 496
Heisenberg algebra 71
Hexagon condition 429—433
Heyting algebra 279
Hilbert space 30 76 151 194 207 217—219 244
Homogeneous space 215—218 277
Homomorphism 2 8 16 350 417
Hopf algebra 7 36 42 48 449 472 476
Hopf algebra map 8
Hopf ideal 11
Ideal 4
Identity element 1 71 195 432 441
Incidence bialgebra 176 210
Incidence coalgebra 175—177
Induced action 339
Induced coaction 331
Input-output symmetry xiii 169 200—201 213 277
Integration 27 182 555 578
Internal hom 459—467 495
Intertwiner 21 157 222 419 432 465 484 518
Invariant vector field 391 402—405 562
Isomorphism 417
Isotopy 447 450
Iwasawa decomposition 250 327 370 377 398 411
Joint system 194—197 203 211 442
Jones polynomial 70
Jordan — Wigner transform 506
Kac algebra 32—34 46 283
Kac — Moody Lie algebra xix 92 411
Killing form 65 92 216 355 365 456
Knizhnik — Zamolodchikov equation 67
Knot 43 447
Lattice model 103 146 163
Lie algebra 15
Lie bialgebra 348
Lie bialgebra, dual quasitriangular 387
Lie bialgebra, exponentiation 403
Lie bialgebra, factorisable 353 372—374 411
Lie bialgebra, quasitriangular 353
Lie bialgebra, triangular 353—356
Lie coaction 382
Lie coalgebra 349
Lie coboundary 356
Lie comodule 382
Lie comodule Lie algebra 382
Lie comodule Lie coalgebra 382
Lie module 19 381
Lie module Lie algebra 381
Lie module Lie coalgebra 382
Linear coordinate function 106 129 151 183 226 251 342 515 516 530 559
Linear map 3 16 227 459
Link 102 449
Logic xv 168 180 207 278 284
Lorentz group 326 376—378 397
Lusztig automorphism 97 269
Lusztig basis 104
Mackey quantisation 224 282
Manin triple 412
Markov process 181 187
Markov process, active 192 306
Markov process, passive 188
Matched pair, coadjoint 385—387 411
Matched pair, exponentiation 281 390—397
Matched pair, gauge fields 247 395 398
Matched pair, groups 236—245 274 297 390—396
Matched pair, Lie algebras 281 348 378—390 393 411
Matched pair, Lie bialgebras 382
Matched pair, Poisson — Lie groups 408 412
Matched pair, quantum groups 298—301 315
Matrix comultiplication 143 150 163 166 321 521 526 560
Maurer — Cartanform 391—393 396 403
Modular form 456
Module 16 21
Module algebra 17 21 438
Module coalgebra 17 21
Momentum group 215 218 228 260 279 336 343
Momentum observable 216—218 272
monodromy 545
Morphism 417
Multiindex 144
Multiplicative dimension 449—452
Multiplicative function 457
Natural equivalence 418—420 424 429
Natural isomorphism 418 460 475
Natural transformation 470
Noncocommutative xiv 38 192 273 485
Noncommutative xiv 106 169 213 347 580
Noncommutative and noncocommutative xiv 34 177 213 276
Noncommutative geometry xiv 15 105
Noncommutativity, inner-outer xviii 500
Null space 11 135 195
Object 416
Observable-state symmetry 201 208 212 244 275
Operator realisation 30 244 542
Opposite bracket 369
Opposite braiding 488
Opposite cobracket 354 370
Opposite coproduct 9 232 480 489
Opposite product 9 232 488 549
Opposite tensor product 429
Pairing See Duality pairing
Pairing of observables and states 200 208 275 277
Partition function 112—114 164 455 456 513
PBW basis 98
Pentagon condition 420—422 474 494
Pentagonal identity 30
Permutation group 98 133 191 .508
Peter — Weyl theorem 454
Phase-space xiv 213—216 270 273 276 280 347
Planck scale xv 271 276 283
Planck's constant xiv 71 213 250 347 455 501
Poisson action 408
Poisson bracket 347 378 401—409
Poisson manifold 401
Poisson map 401 408
Poisson — Hopf algebra 407
Poisson — Lie group 67 348 402—404 412
Pontryagin duality 13 426
POSET 175
Position observable 183 216—219 336 342
Positive state 204
| Primitive element 15
Principle of self-duality See Self-duality
Probability space 182 186
Pull-back 17 222 471 486
Pure copositive element 204 207
Pure state 195 201 203
Purely quantum phenomenon 580
Push-out 23
q-binomial 85 94 100 507 543
q-commutator 98
q-deformation xvi 164 327 454 500 504 557 576 580
Q-differentiation 80 82 306 345 542 578
q-dimension 495
q-direct sum 579
q-Euclidean space 501 522 563—570 574 579
Q-exponential 83 551
q-exterior algebra 559
q-harmonic oscillator 79—82 103 504
q-Hecke algebra 466
q-Heisenberg algebra 73—79 102
q-integer 452 542
q-integration 103 579
q-Lorentz group 318 321—327 336 345 574
q-Minkowski space 337 346 501 522 530 564 570—590
q-Poincare algebra 412 521—524 565 568 572 574 577—580
q-quantum mechanics 346
q-regularisation xvii 455
q-rotation group 136
q-Serre relation 96
Quadratic algebra 141—143 526 578
Quantisation problem 218—220 222- 227
Quantum  131
Quantum algebra of observables 217
Quantum Casimir 89 145 578
Quantum combinatorics 169
Quantum covector 107 150—153 160 438
Quantum determinant 129—137 164 406 535 558 563 574
Quantum dimension 451 458
Quantum double See Double quantum group
Quantum Fourier transform 14 43
Quantum group xi 35
Quantum group gauge theory 257 259 282
Quantum group normalisation 126 128 518
Quantum group, enveloping algebra type 69 92—99 118 142 357
Quantum group, factorisable 43 52 67 96 143 226 290 334 345 490 497
Quantum group, function algebra type 105 132—136 405
Quantum group, nonstandard 122 137
Quantum group, real form See *-quantum group
Quantum group, strict xii 35 105 429 453
Quantum group, triangular 43 59 67 251 433 484 494
Quantum inverse scattering xiii 103 147 163—166 286 412
Quantum Iwasawa decomposition 318 327
Quantum Killing form 43 67 101 290 331 484 490
Quantum kinematics 196 217
Quantum Lie algebra 143—145 165
Quantum line 46 50 310—313 523
Quantum linear transformation 154 162 166
Quantum Mach's principle 201 281 412
Quantum matrix 107—116 130 150 559—563
quantum mechanics 108 169 194 200 213 270 277 283
Quantum metric 136 525 530 554 577
Quantum optics 71 211
Quantum order 453—457 495
Quantum plane 9 103 153 501 514
Quantum probability 210
Quantum random walk 197—199 209
Quantum reflection 97
Quantum state xv 202 208 219 456
Quantum stochastic process 210
Quantum superplane 156 515
Quantum symmetry 47 285—287 499
Quantum trace 451 458 534
Quantum vector 107 150—153 159—161 459 578
Quantum Weyl group xviii 97 104 269 282 311
Quantum Wick rotation 574 580
Quantum-geometry transformation 327 580
Quasi-Hopf algebra 62—66 474
Quasibialgebra 422
Quasisymmetry See Braiding
Quasitriangular Hopf algebra See Quasitriangular structure
Quasitriangular structure 35—38 44 62 164 353 404 415 432 472 509
Quasitriangular structure, antireal 44 88
Quasitriangular structure, factorisable 43 52 67 96 140 226 290 334 345 353 368 372—374 411 490 497
Quasitriangular structure, real 44 87
R-matrix, antireal-type 291 320 339 362 376
R-matrix, biinvertible 127 458 476 526 531 570
R-matrix, gluing 579
R-matrix, multiparameter 137 153 164 567 573
R-matrix, nonstandard 122 134 153 164 505 530 567 573 577
R-matrix, normalisation 115 126 128 518
R-matrix, real-type 140 321 362—365 528 570
R-matrix, regular 126 518 531 561
R-matrix, second inverse 127
R-matrix, triangular 123
R-matrix, universal See Quasitriangular structure
Random variable 169 181 194 206
Random walk xiii 169 181—183 200
Random walk, nonstationary 189 192 203 206—208
Random walk, stationary 188
Real form, compact 140 365 377 386 409
Real form, Lie algebra 82 86 361
Real form, Lie bialgebra 363—365 375 386
Real form, quantum group See *-quantum group
Reconstruction 416 467
Reconstruction, braided group 478—489
Reconstruction, quantum group 467—473
Reconstruction, quasi-Hopf algebra 474
Rectangular quantum matrix 159 163 167 563
Regular isotopy 447
Regularly isomorphic extensions 256
Reidemeister move 447—449
Representation 2 16 89 93 414 421 435 465
Representation, adjoint 18 21 143 293 328 339 350 385 432 483 497
Representation, canonical 116 137
Representation, coadjoint 18
Representation, cocycle 269
Representation, conjugate 415 450
Representation, conjugate fundamental 111 137 518 522
Representation, fundamental 111 137 518 520
Representation, of category 424
Representation, of cross product 221
Representation, regular 18 21 28 189 195 225—227 419 453
Representation, tensor product xii 21 421
Representation, unitary 86 139 223
Representing object 460 470
Reversal of arrows 323 330
Ribbon element 42 52 67 101
Ribbon transformation 447
Rigid object 443 448
Ring 2
Root of unity 70 80 89 99—102 104 309 510
Root vector 93 363 370
Rooted tree 177
S-Hermitian element 204
Schroedinger representation 79 222—228 293 453
Schur — Weyl duality 466 496
Self-duality, braided group 490 497
Self-duality, category 277
Self-duality, Lie bialgebra 358
Self-duality, principle xiii 213—215 271 277—280
Self-duality, quantum group 10 43 67 214 248 305 309 313
Semiclassical limit 123 129 145 347 357
Semidirect product See Cross product
Semidirect sum See Cross sum
Semigroup 1
Serre relation 93 96 309 364
Set 170 175 181 419
Shuffle bialgebra 210
Six-vertex model 149
Skew-antipode 10
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