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Majid S. Ч Foundations of Quantum Group Theory
Majid S. Ч Foundations of Quantum Group Theory

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Ќазвание: Foundations of Quantum Group Theory

јвтор: Majid S.

јннотаци€:

This is a graduate-level text that systematically develops the foundations of the subject. Quantum groups (i.e. Hopf algebras) are treated as mathematical objects in their own right; basic properties and theorems are proven in detail from this standpoint, including the results underlying key applications. After formal definitions and basic theory, the book goes on to cover such topics as quantum enveloping algebras, matrix quantum groups, combinatorics, cross products of various kinds, the quantum double, the semiclassical theory of Poisson-Lie groups, the representation theory, braided groups and applications to q-deformed physics. The explicit proofs and a great many worked examples and exercises will allow readers to quickly pick up the techniques needed for working in this exciting new field.


язык: en

–убрика: ћатематика/јлгебра/ вантовые группы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1995

 оличество страниц: 627

ƒобавлена в каталог: 19.03.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$\mathcal C^*$ algebra      32Ч34 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 16Ч22 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 Ч Kostant Ч Symes theorem      409Ч412
Affine quantum group      104
Alcove      455
Alexander Ч 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      171Ч173
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      380Ч383 388
Bicrossproduct Poisson Ч Lie group      409
Bicrossproduct quantum group      213 230Ч245 270 280Ч283 399 412
Biideal      11 100 135
Bimodule      293 423
Binomial bialgebra      172Ч175 177
Biproduct      346
Birman Ч Murakami Ч 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 528Ч531 534 553 578
Bosonisation      xviii 20 328 491Ч493 498 505 510 519Ч522 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 570Ч574
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 527Ч530 537
Braided approach      xviii 500 559 577Ч580
Braided bialgebra      476
Braided binomial theorem      545Ч548 552
Braided coaddition      163 512Ч515 539 543 559 564 570 577Ч580
Braided cocommutative      481 491 497
Braided coform      557
Braided combinatorics      547
Braided commutative      486
Braided comultiplication      143 526 571 578
Braided covector      512Ч516 534
Braided cross product      491 497 542
Braided determinant      143 337 528 535
Braided differential form      516 557 562 566 572
Braided differentiation      526 539Ч543 556
Braided electromagnetism      559
Braided epsilon tensor      558
Braided exponential      549Ч553 578Ч580
Braided exterior algebra      558
Braided factorial      548
Braided Fourier transform      104
Braided Gaussian      554Ч555 578 580
Braided group      163Ч165 230 286 328 346 371 415 467 476 481Ч499
Braided group, enveloping algebra type      335 483
Braided group, function algebra type      487
Braided Hopf algebra      See Braided group
Braided integer      540Ч547 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 144Ч146 165 497
Braided line      9 510 542 549 559
Braided linear algebra      501 526 533Ч539 549 578
Braided linear transformation      536
Braided mathematics      498
Braided matrix      141Ч146 162 334 341 346 488 498Ч501 526 570 578
Braided metric      525
Braided plane      9 514
Braided quantum group      486Ч489 497
Braided quantum mechanics      542
Braided Taylor's theorem      550 553
Braided tensor product algebra      167 415 438Ч441 476Ч479 495 500
Braided vector      516Ч517 534
Braided Weyl algebra      542
Braiding      xii 415 430Ч438
Brownian motion      169 182Ч186
Canonical element      90 463
Cartan generator      92 99 296 370
Cartan matrix      92 103 309 370
Categorical dimension, rank      416 445Ч458 495
Categorical dual quantum group      233 323 338
Categorical trace      445
Category      414Ч419
Category, abelian      428 438
Category, braided      415 429Ч431 438 444 450 494Ч496
Category, linear      428
Category, monoidal      278 420Ч431
Category, quasitensor      See braided
Category, ribbon      447Ч451 495
Category, rigid      443Ч445 472Ч474 479 495 549
Category, small      417
Category, symmetric tensor      430Ч433 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 204Ч207 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 409Ч412
Classical limit      See Semiclassical limit
Clebsch Ч Gordan coefficient      428 436
Cleft extension      257Ч259 282 307
Co-Jacobi identity      349Ч351 364 404
Coaction      22Ч27 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      53Ч55 65 255 267 350
Coboundary Lie bialgebra      351Ч355
Cobracket      350 355 363 382 404
Cochain      53 351
Cocommutative      12 33 61 193 226 229 253 294 485
Cocommutator      349
Cocompletion      486
Cocycle      53Ч55 253 260 392
Cocycle action      253 260 268
Cocycle bicrossproduct      266Ч268
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      443Ч449 462 479 551Ч553
Coherence      419 424 431 444 447Ч449 494
Cohomology of group      33 54 402
Cohomology of Lie algebra      54 61 350 393
Cohomology of quantum group      55Ч63 68 252 258Ч262 282
Cohomology of quasi-Hopf algebra      65
Cohomology, non-Abelian      67 253Ч255 282
Cologic      181
Combinatorics      170Ч179 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 318Ч327 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      47Ч49 52 66 127 184Ч189
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      330Ч335 483
Covariantised, braided product      329Ч335 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      293Ч295 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 476Ч478 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 370Ч375 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 298Ч301 333 343 571
Double cross sum      367 372 379Ч384 387Ч389 409 411
Double group algebra      226 294 435
Double Lie bialgebra      348 366Ч369 378 387 411
Double matched pair      388 412
Double Poisson Ч Lie group      409
Double quantum group      90 96 215 284Ч290 343 432 453 493 549
Double quantum group as cocycle extension      305
Double quantum group as complexfication      318
Double quantum group as cross product      327Ч336 339Ч341
Double quantum group as quantum mechanics      226 336 341
Double quantum group as twisting      297 310
Double quantum group, generalised      287 303Ч305 315 344
Dressing action      409
Drinfeld Ч Jimbo solution      363
Dual homogeneous space      xiv 215 277
Dual Lie bialgebra      350
Dual monoidal category      278 284 424 431 494
Dual object      442Ч450 509
Dual Poisson Ч Lie group      406
Dual quantum group      10 125 214 233 338 400
Dual quantum system      287
Dual quasitriangular structure      35 48Ч50 61 67 112 126 164 319 328 357 387 437Ч440 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 206Ч208 213Ч215 271Ч277
Dynamical system      xv 219 328
Eight-vertex model      122 149
Einstein's equation      xiv 215 275Ч279 521
Elliptic function      149
Endomorphism      16 227
entropy      174 201
Evaluation map      443Ч449 553
Evolution of joint system      196
Exactly solvable      103 115 146Ч149 163 347 401 405 410 455
expectation value      182 192 200 219 456
Exponential map      229
Extension theory      252 269
Extension theory, algebra      257Ч261
Extension theory, group      266
Extension theory, Lie algebra      267
Extension theory, Lie bialgebra      383
Extension theory, quantum group      264Ч268 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 Ч Reshetikhin Ч Takhtajan generators      108 118 133Ч136 164 325 335
Fermion      143 154Ч156 174 415 442 500Ч502 506 516 557
Field      2
Figure of eight      451
Fixed point subalgebra      257Ч259 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
1 2 3
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