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Kassel C. — Quantum Groups
Kassel C. — Quantum Groups



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Название: Quantum Groups

Автор: Kassel C.

Аннотация:

This book provides an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and on Drinfeld's recent fundamental contributions. The first part presents in detail the quantum groups attached to SL[subscript 2] as well as the basic concepts of the theory of Hopf algebras. Part Two focuses on Hopf algebras that produce solutions of the Yang-Baxter equation, and on Drinfeld's quantum double construction. In the following part we construct isotopy invariants of knots and links in the three-dimensional Euclidean space, using the language of tensor categories. The last part is an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations, culminating in the construction of Kontsevich's universal knot invariant.


Язык: en

Рубрика: Математика/Алгебра/Квантовые группы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 552

Добавлена в каталог: 26.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(N)_q$      74
$A(c)$      188 194 197
$A^{\times}$      9
$A_{g,t}$      449 458 459 468 471
$Br(C,D)$      327
$B^n(g,M)$      421
$B_n$      263 377 454 459
$B_q$      224 227
$C$      100 404 412 461
$C(F)$      297
$C[[h]]$      385
$C^n(g,M)$      420
$C_h$      412
$C_q$      131—133
$D(B)$      365 366
$Gl(2)$      99
$Gl(n)$      94
$Gl(V)$      94
$GL_q(2)$      83 87 196
$GL_q(n)$      91
$gr(A)$      14
$H^n(g,M)$      421
$L(A)$      94
$M(2)$      10 33 47 57 65 112
$M(n)$      47
$M_q(2)$      78 83 89 150 194 418
$M_q(n)$      91 198
$M_{p,q}(2)$      90 198
$Prim(C)$      48
$Prim(H)$      495
$P_n$      454
$Q_{g,V}$      411 418 486 503
$R_h$      409 412 458 359
$R_{KZ}$      371
$Sl(2)$      99 405 412
$Sl(n)$      94
$SL_q(2)$      83 87 90 153 196 366 418
$SL_q(n)$      91 163
$SL_{p,q}(2)$      91
$T'(V)$      67
$Tens(\mathcal{C},\mathcal{D})$      288
$Tens_{str}(\mathcal{C},\mathcal{D})$      288
$Tr_q$      353 363
$U(sl(2))$      99 109 113 118
$U_h$      412
$U_h(g)$      407 319 430 458
$U_h(sl(2))$      412 419
$U_q$      125 139 143
$U_q(g)$      138 419
$U_q(sl(2))$      121 122 138 140 153 162 168 223 412
$U_q(sl(l+1))$      139
$U_q(sl(n))$      163
$V(n)$      102 118 417
$V(X)$      129
$V_\lambda$      406 409 417
$X(G)$      319
$X_G(G)$      319 360
$X_n$      267 269 454 479
$YB{C)$      324
$Y_n$      267 270 452 454
$Z^n(g,M)$      321
$Z_q$      133
$[N]$      121
$\mathbf{V}(X)$      129 138
$\mathbf{Z}(C)$      330
$\mathbf{Z}(K)$      490 505
$\mathbf{Z}[X_G(G)]$      360
$\mathcal{C}^{rev}$      337
$\mathcal{C}^{str}$      288 337 377
$\mathcal{D}(A)$      333
$\mathcal{R}$      313 358 311 501
$\Phi$      369 443 465
$\Phi(A,B)$      465 469 479
$\Phi_F$      373
$\Phi_{KZ}$      459 463 469 471 478 498
$\Phi{m,q}$      255 313 418 486
$\rho^{A}_{n}$      378
$\rho^{C}_{n}$      377
$\rho^{KZ}_{n}$      456 457 459
$\rho^{R_{h}}_{n}$      459
$\tau$      299 305 312 360
$\tau(p_1,q_1,...,p_k,q_k)$      466 482
$\tilde{M}$      388
$\tilde{V}_n$      317
$\tilde{V}_\lambda$      409
$\tilde{\bigotimes}$      390 410
??      136 224 230 238 364
A      500
A-operation      243 259
Abelian Lie algebra      94 95 117
Acyclic chain complex      447
Adjoint corepresentation      236
Adjoint functors      279 291 400
Adjoint representation      99 107 208 404 429
Adjoint representation of a Lie algebra      208
Affine line      8
Affine plane      8 65 109
Alexander polynomial      246 486
Algebra      3 39
Algebra of differential operators.      21
Algebra of pseudo-differential operators      21
Algebra topologically generated by generators ad relations      407
Antilinear      86
Antipode      50 52 55 58 84 197
Antisymmetric tensors      37
Antisymmetrization      436
Associativity constraint      281 369 377 460 499
At?      496
Autonomous tensor category      347 353 380
B      321
Bar complex      437 447
Basic hypergeometric series      90
Basis of a free module      26
Bialgebra      46 58 83 285 493
Bialgebra of a monoid      46 51
Bicrossed product of bialgebras      204 213
Bicrossed product of groups      201
Bimodule      71
Binomial coefficients      74 122
Braid      262 307
Braid, category      321 325
Braid, diagram      263 313
Braid, group      264 272 307 377 395 454 499
Braid, group relations      265 327
Braid, group representation      395 459
Braid, group representation associated to a braided quasi-hialgebra      378
Braid, group representation associated to a braided tensor category      377
Braided bialgebra      173 175 177 178 198 318
Braided Hopf algebra      173 175 183 216 229 333 361 365
Braided quasi-bialgebra      371 376 377 394
Braided quasi-Hopf algebra      379 380 382
Braided tensor category      315 327 329 330 338 341 371 376 377 410 460 495 498
Braided tensor, equivalence      376 460
Braided tensor, functor      327 329
Braiding      315 341 377 410 460 495 499
Burau representation      269 272
Canonical 2-tensor      412 449 460
Canonical 2-tensor of a quantum enveloping algebra      397
Cartan matrix      139 405 407
Casimir element      100 103 404 412 427 461 496
Category      275
Category, associated to a family of groups      276
Category, of ribbons      358 501
Central element      503
Centre      4 90 100 117 130 133 134 139 181 404 410 412 431 503
Centre (cont.) of a tensor category      330 333 338 366
Centre (cont.) of the braid group      269
Chain complex      447
Chain map      447
Chord diagram      487 491
Classical limit of a quantum enveloping algebra      397
Clebsch — Gordan      157
Clebsch — Gordan formula      105
Closed polygonal arc      242
Closure of a braid      272 307
Closure of a ribbon      359
Coaction      62
Coadjoint corepresentation      236
Coadjoint representation      210 429
Coalgebra      40 431
Coalgebra of a set      41 42 46 292
Coassociative      40 43
Cobar complex      432 434 445 447
Coboundary      421
Cobraided bialgebra      184 191 195 197 198 237 238
Cochain complex      447
Cocommutative bialgebra      58 174 318
Cocommutative coalgebra      40 44
Cocommutative Hopf algebra      350 495
Coefficient space of a representation      71
Coevaluation map      29 60 306 347
Cohomology group      447
Cohomology of a coalgebra      431
Cohomology of a Lie algebra      421 446
Coideal      43
Combinatorially equivalent links      243
Combinatorially equivalent tangles      259
Commutative algebra      4 40
Commutative bialgebra      63
Commutativity constraint      314
Comodule      62 366
Comodule-algebra      64 65 85 89 91
Comodule-coalgebra      236
Comparison theorem      448
Complete module      388 390
Completely reducible representation      5
Composition of tangles      261 299
Comultiplication      40 285 368
Concatenation      7 299
Configuration space      267 269 479
Congruent words      298
Connected component of a link      242
Connection      450
Convolution      49 69 237 479
Convolution algebra      68
Conway, polynomial      246 253 486
Conway, triple      252 313 486
Coproduct      40
Coribbon algebra      365
Counit      40 285 368
Counital      40 44
Crossed bimodule      220 237 238 333 414
Crossed G-set      319 338 360
Crossed product of bialgebras      207 215 238
Crossing point      246 260
Curvature of a connection      451
CYCLE      421
Dehn's theorem      245
Derivation      14 21 108 117 118 146 421
DET      79
Differential form      450 480
Differential graded algebra      432 435
DIM      358 363 364 411
Direct product of groups      401
Direct product of vector spaces      25 292
Direct sum of vector spaces      25 292
Dominant weight      406 409 431
Drinfeld associator      369 373 465 478 479 498
Drinfeld quantum double      333 380
Drinfeld series      478 498
Drinfeld — Jimbo algebra      139 163 366 407 430 449
Drinfeld — Kohno theorem      459 460
Dual vector space      27 41 46 59 62 66 71 99 110 115 118 154 177 182 347
Duality      120
Duality between bialgebras      110 112 114
Duality between Hopf algebras      150 153 163
EDGE      242
Element $\theta$      9 410
Element t      405 455 459 461
Element u      180 183 410
Embedding of a chord diagram      487
Endomorphism      276
Endpoint of a simple polygonal arc      242
Enhanced R-matrix      306 307 311 313
Enveloping algebra      94 97 292 395 406
Equivalence of categories      278
Equivalent braided quasi-bialgebras      376 378
Equivalent, links      244
Equivalent, quasi-bialgebras      375
Equivalent, tangles      260
Equivalent, words      295
Essentially surjective functor      278
Evaluation map      28 60 182 306 347
Exponential function      392
Extension of Lie algebras      422
Exterior algebra      37 435
Faithful functor      278
Filtered algebra      13
Flat connection      451 452 456
Flip      4 24 40 58 63 168 314 318 393 457 495
Formal series      385
Four-term relation      488 492 498
Framed singular knot      484
Framed tangle      270 313 358
Free algebra      7 13 119 280
Free comodule      63 70
Free Lie algebra      119
Free module      26
Free tensor category on a class of morphisms      297
FRT construction      188 194 198
Fully faithful functor      278
functor      277
Fundamental group of a link      245 361
Fundamental group of a topological space      269 270 274 451 454
G-invariant      435
Gauge transformation      373 381 394 399 442 460
Gauss polynomials      74
Generators of a strict tensor category      297
Generic isotopy      250
Generic link diagram      249
Generic tangle diagram      261
Graded algebra      12
Graded coalgebra      68 436
Graded dual vector space      67 436
Graded tensor product      292 436
Graded vector space      292
Grouplike element      56 292
Groupoid      276 279
Groupoid of isomorphisms      277
H-adic completion      388 390 401
H-adic topology      387 388 401 407
Harish — Chandra homomorphism      131 139
Heisenberg Lie algebra      398
Hexagon axiom      315 372
Highest weight, module      127 130 131 138
Highest weight, vector      101 127 154 406 410
Hilbert's basis theorem      19 22
Holonomy group      450
Homfly polynomial      253
Homology group      447
Hopf *-algebra      87 90 92 118 119 162 163
Hopf algebra      185 196 197 365
Hopf algebra of a group      51 56 219
Hopf link      245 256 313 361
Hornotopy      273 448 451
Hyperlogarithm      481
Identity morphism      276
Indecomposable module      5
Infinitesimal braid group relations      454 478 492
Infinitesimal braiding      494 497
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