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| Majid S. — Foundations of Quantum Group Theory |
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| Предметный указатель |
 algebra 32—34 105 169 212 218
*-action 223
*-algebra 30
*-algebra, Hermitian type 146
*-algebra, unitary type 140
*-braided group 528
*-pairing 30
*-quantum group 30 87 139 342
*-quantum group, antireal 44 88
*-quantum group, nonstandard 101
*-quantum group, real 44 87
*-representation 139 223
Abelian group 1 13 45 50 193 266 279 416
Abelian Lie algebra 267 305
action 2 16—22 216 494
Action, adjoint 18 21 143 293 328 339 350 385 432 483 497
Action, coadjoint 18 144 226 286 301 328 348 385 411 487
Action, coregular 18 29 207 224 244 294 306
Action, regular 18 21 28 189 195 225 419 453 483
Adjoint morphism 443
Adler — Kostant — Symes theorem 409—412
Affine quantum group 104
Alcove 455
Alexander — Conway polynomial 70 156 165 530
Algebra 3 257 419 423 438
Algebra map 4
Algebraic model 126 184 219 227 273 399 407 509
Anomaly 260
Antialgebra map 7
Anticoalgebra map 7
Antiinvolution 86
Antipode xii 7
Antipode, inverse 7 40 49 235 343 427
Antipode, skew 32 427 432 450 463
Antipode, square of 99 266 269
Antipode, weak 127 164 296 314 344
Anyonic line 507
Anyonic quantum group 507
Anyonic tensor product algebra 440 506
Anyonic vector space 433 451 506
Automorphism braided group 481 486
Axioms as arrows xiii 10 23 47 62 316 418
Background quantum group xvii 150 510 525 548 556 561 565 571
Background quantum group, anyonic 38 433 507
Background quantum group, super 415 434 502 505
Bag model 171—173
Bialgebra 6 421 471
Bicharacter 45 48 50 112 553
Bicomodule 157
Bicomodule algebra 157
Bicovariant algebra 150 158 167
Bicovariant differential form xviii 165 578
Bicross sum 380—383 388
Bicrossproduct Poisson — Lie group 409
Bicrossproduct quantum group 213 230—245 270 280—283 399 412
Biideal 11 100 135
Bimodule 293 423
Binomial bialgebra 172—175 177
Biproduct 346
Birman — Murakami — Wenzl algebra 467
Black hole xv 250 273
Blackboard framing 448
Boltzmann constant 455
Boltzmann weight 146
Boolean algebra 169 207 278
Boolean coalgebra 171 176
Boson 174 415 502 528—531 534 553 578
Bosonisation xviii 20 328 491—493 498 505 510 519—522 549 565 572
Braid 430 444
Braid group 431 466 547
Braid statistics 143 174 415 441 500 515 532 543 578
Braid statistics, additive 515 539 560 564 570—574
Braid statistics, multiplicative 501 527 571
Braided addition law 515 539 543 559 577
Braided adjoint action 497
Braided adjoint coaction 538
Braided algebra 438
Braided antipode 143 479 488 492 508 512 527—530 537
Braided approach xviii 500 559 577—580
Braided bialgebra 476
Braided binomial theorem 545—548 552
Braided coaddition 163 512—515 539 543 559 564 570 577—580
Braided cocommutative 481 491 497
Braided coform 557
Braided combinatorics 547
Braided commutative 486
Braided comultiplication 143 526 571 578
Braided covector 512—516 534
Braided cross product 491 497 542
Braided determinant 143 337 528 535
Braided differential form 516 557 562 566 572
Braided differentiation 526 539—543 556
Braided electromagnetism 559
Braided epsilon tensor 558
Braided exponential 549—553 578—580
Braided exterior algebra 558
Braided factorial 548
Braided Fourier transform 104
Braided Gaussian 554—555 578 580
Braided group 163—165 230 286 328 346 371 415 467 476 481—499
Braided group, enveloping algebra type 335 483
Braided group, function algebra type 487
Braided Hopf algebra See Braided group
Braided integer 540—547 550
Braided integrability 550
Braided integration 555 562 566 572 578
Braided Leibniz rule 103 524 541 554 561 565 571
Braided Lie algebra 121 144—146 165 497
Braided line 9 510 542 549 559
Braided linear algebra 501 526 533—539 549 578
Braided linear transformation 536
Braided mathematics 498
Braided matrix 141—146 162 334 341 346 488 498—501 526 570 578
Braided metric 525
Braided plane 9 514
Braided quantum group 486—489 497
Braided quantum mechanics 542
Braided Taylor's theorem 550 553
Braided tensor product algebra 167 415 438—441 476—479 495 500
Braided vector 516—517 534
Braided Weyl algebra 542
Braiding xii 415 430—438
Brownian motion 169 182—186
Canonical element 90 463
Cartan generator 92 99 296 370
Cartan matrix 92 103 309 370
Categorical dimension, rank 416 445—458 495
Categorical dual quantum group 233 323 338
Categorical trace 445
Category 414—419
Category, abelian 428 438
Category, braided 415 429—431 438 444 450 494—496
Category, linear 428
Category, monoidal 278 420—431
Category, quasitensor See braided
Category, ribbon 447—451 495
Category, rigid 443—445 472—474 479 495 549
Category, small 417
Category, symmetric tensor 430—433 502
Category, tensor See Symmetric tensor
Category, tortile See Ribbon
Central element 69 89 132 145 519 528 574 578
Central extension 252 266 308 312 344 523
Centre of mass 78
CHARACTER 13 204—207 455 470
Character formula 104
Characteristic zero 2
Chevalley generator 92 364
Classical algebra of observables 216
Classical data 216
| Classical inverse scattering 215 371 378 401 409—412
Classical limit See Semiclassical limit
Clebsch — Gordan coefficient 428 436
Cleft extension 257—259 282 307
Co-Jacobi identity 349—351 364 404
Coaction 22—27 154 536
Coaction, adjoint 24 26 162 302 328 385 487 535 538
Coaction, coadjoint 25 163 339 341
Coaction, coregular 24
Coaction, regular 24 26 157 257 432
Coalgebra 5
Coalgebra map 6
Coassociativity 5
Coboundary 53—55 65 255 267 350
Coboundary Lie bialgebra 351—355
Cobracket 350 355 363 382 404
Cochain 53 351
Cocommutative 12 33 61 193 226 229 253 294 485
Cocommutator 349
Cocompletion 486
Cocycle 53—55 253 260 392
Cocycle action 253 260 268
Cocycle bicrossproduct 266—268
Cocycle comodule coalgebra 261
Cocycle cross coproduct 261
Cocycle cross product 68 252 262 269 282
Cocycle module algebra 253 260
Codouble Lie bialgebra 370
Codouble quantum group 286 297
Coentropy 206
Coevaluation map 443—449 462 479 551—553
Coherence 419 424 431 444 447—449 494
Cohomology of group 33 54 402
Cohomology of Lie algebra 54 61 350 393
Cohomology of quantum group 55—63 68 252 258—262 282
Cohomology of quasi-Hopf algebra 65
Cohomology, non-Abelian 67 253—255 282
Cologic 181
Combinatorics 170—179 194 200 210
Commutant 466
Commutative 12 33 54 68 108 121 169 199 253 530 580
Comodule 22 26
Comodule algebra 26 440 518
Comodule coalgebra 26
Compact matrix pseudogroup 34
Completely integrable See Exactly solvable
Complexification 86 286 318—327 345 375 386 412
Comultiplication xiii 5
Conditional expectation 194 203 211
Conditionally positive map 211
Configuration space 181 182
Conformal field theory xix
Conjugate bosonisation 524
Convex linear combination 189
Convolution algebra 47—49 52 66 127 184—189
Convolution-inverse 49 60 109 114 127 259 296 486
Copairing 317 321 553
Copositive element 204
Coproduct xiii 5
Corepresentation 22 458 520
Coroot 92 98 456
Counit 5
Counital cocycle 53
Covariant algebra 20 160 415 438
Covariantised, braided coproduct 330—335 483
Covariantised, braided product 329—335 487
Creation process 206
Cross coproduct 25 214 230 262 308 332 491
Cross product 19 22 214 222 227 252 282 328 346 398 491
Cross sum 374 381 411
Crossed module 293—295 344 427 432 494
Current algebra 410
Deconstruction 272
Deformation cohomology xviii 68
Deformation parameter 70 325 347 358 405 499 509
Diagram commutes 3
Diagrammatic notation 439 444 448 476—478 497
Diffeomorphism Lie bialgebra 411
Differential graded algebra, xviii 558
Diffusion equation 169 186 199
Dilaton, dilatonic extension 50 510 519 532 565 571 577
Direct sum 2 367 370—375 408 428 438 454
Distributive lattice 168 171
Double bialgebra 428
Double category 426
Double cross cobracket 371 409
Double cross coproduct 286 316 334 345
Double cross product group 245 281 378 399 413
Double cross product Poisson-Lie group 408
Double cross product quantum group 116 280 285 298—301 333 343 571
Double cross sum 367 372 379—384 387—389 409 411
Double group algebra 226 294 435
Double Lie bialgebra 348 366—369 378 387 411
Double matched pair 388 412
Double Poisson — Lie group 409
Double quantum group 90 96 215 284—290 343 432 453 493 549
Double quantum group as cocycle extension 305
Double quantum group as complexfication 318
Double quantum group as cross product 327—336 339—341
Double quantum group as quantum mechanics 226 336 341
Double quantum group as twisting 297 310
Double quantum group, generalised 287 303—305 315 344
Dressing action 409
Drinfeld — Jimbo solution 363
Dual homogeneous space xiv 215 277
Dual Lie bialgebra 350
Dual monoidal category 278 284 424 431 494
Dual object 442—450 509
Dual Poisson — Lie group 406
Dual quantum group 10 125 214 233 338 400
Dual quantum system 287
Dual quasitriangular structure 35 48—50 61 67 112 126 164 319 328 357 387 437—440 475 518 578
Dual quasitriangular structure, antireal 52
Dual quasitriangular structure, real 52 140 320
Dual triangular structure 52 357
Dual vector space 3 443
Duality functor 444
Duality pairing 11 13 67 116 181 277 287 319 451 523 548
Duality principle xiii 200 206—208 213—215 271—277
Dynamical system xv 219 328
Eight-vertex model 122 149
Einstein's equation xiv 215 275—279 521
Elliptic function 149
Endomorphism 16 227
entropy 174 201
Evaluation map 443—449 553
Evolution of joint system 196
Exactly solvable 103 115 146—149 163 347 401 405 410 455
expectation value 182 192 200 219 456
Exponential map 229
Extension theory 252 269
Extension theory, algebra 257—261
Extension theory, group 266
Extension theory, Lie algebra 267
Extension theory, Lie bialgebra 383
Extension theory, quantum group 264—268 272 305
Faa di Bruno bialgebra 176 194 210
Factorisable See Quasitriangular structure
Factorisation problem, algebra 31 441
Factorisation problem, group xiv 214 274 327 409
Factorisation problem, quantum group 286 297 299 327
Faddeev — Reshetikhin — Takhtajan generators 108 118 133—136 164 325 335
Fermion 143 154—156 174 415 442 500—502 506 516 557
Field 2
Figure of eight 451
Fixed point subalgebra 257—259 465
Flow 216
Fock representation 76 120 195 206 211
Fourier transform 14 42 190 279 416 426 470 496 508 559 579
Framed knot 448
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