Kassel C. — Quantum Groups :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

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Предметный указатель

Infinitesimal symmetric category      495 498 500 502 528
Inner derivation      421
Invariant of finite degree      485 505
Invariant symmetric 2-tensor      397 499
Inverse limit      386 401
Inverse limit, topology      402
Inverse system      400 401
Irreducible representation      5
Isomorphism      276
Isotopic link diagrams      249
Isotopic links      243
Isotopic tangles      260
Isotopy      243 260 268 299
Isotopy, invariant      244 273 305 360 367 410 418 485
Isotopy, invariant of finite type      485
Iterated integral      465 480
Jbnes — Conway polynomial      253 312 486
Jones polynomial      253 486
Jones polynomial, two-variable      253
Kauffman's bracket      270 272
Killing form      404 405
Knot      242
Kontsevich universal knot invariant      490 500 504 505
Koszul complex      439
Laurent polynomials      9
Left duality      342 366 380 410 502
Left unit constraint      282 315 369
Leibniz formula      21
Lie algebra      93 292 395 420 455
Link      242 258 300 305
Link diagram      246
Link projection      246
Linking number      245
Loop      267 273 456
Mac Lane's coherence theorem      291 293
Markov's theorem      273
Matched pair of bialgebras      203 211
Matched pair of groups      200 207
Milnor and Moore, theorem of      494
Minimal braided Hopf algebra      238
Mirror image      253 257
Module      4 61
Module over a Lie algebra      98
Module-algebra      107—109 117 118 148
Module-coalgebra      203 236
monodromy      451 454—456 458 459 469
Monoidal category      293
Morphism of a category      275
Morphism of algebras      3 40
Morphism of bialgehras      46 69
Morphism of braided quasi-hialgebras      372
Morphism of coalgebras      41 45
Morphism of comodules      62
Morphism of Hopf algebras      51 69
Morphism of modules      5 61
Morphism of quasi-bialgebras      371
Morphism of topological algebras      392
Morphism of topological braided quasi-bialgebras      394
Morphism of topological quasi-hialgebras      393
Multiple zeta value      465 466 483
Natural isomorphism      277
Natural tensor, isomorphism      288
Natural tensor, transformation      287
Natural transformation      277
Noetherian      18 21 73 81 118 123
Non-commutative residue      22
Object of a category      275
Opposite algebra      4
Opposite coalgebra      41
Opposite Lie algebra      94
Order of a link      242 244
Ore extension      15 19 22 73 81 91 123
Oriented link      242
Origin of a simple polygonal arc      242
Overcrossing      246 260
Parallel transport      450
Partial trace      31 306
Partial transpose      306
Partial transposition      30
Pentagon axiom      282 293 369
Perfect duality      110
Permutation of a braid      267 321 499
Picard's method of approximation      466 481
Piecewise-linear      242
Poincare series      20
Poincare — Birkhoff — Witt theorem      98
Polygonal arc      242
Polylogarithm      482
Polynomial algebra      8 13
Presentation of a strict tensor category by generators and relations      298 300 302 303 313
Primitive element      48 119 397 446 494 495 505
Product of categories      276
Product of groups      202
Product of loops      268 273
Product, algebra      4
Pure braid group      270 454
q-analogue      411
Q-binomial formula      74
Q-Chu — Vandermonde formula      75
Q-difference equation      90
Q-differentiation      89 90
Q-exponential      76 90
q-factorial      74
Q-hypergeometric series      90
Q-Pascal identity      74
Quadratic algebra      91
Quantization      397 460
Quantum      3
Quantum -symbols      158
Quantum Casimir element      130 132 139 144 412
Quantum Clebsch — Gordan coefficients      158 161 163
Quantum determinant      79 84 91 152 195
Quantum dimension      358 360 363—365 411 417 504
Quantum double      213 215 216 219 227 238 366 414 419
Quantum enveloping algebra      395 399 401 408 430 442 449 459
Quantum group invariant      486 503
Quantum partial derivative      147
Quantum plane      72 85 118 146 148
Quantum trace      354 359 363 504
Quantum Yang — Baxter module      238
Quasi-bialgebra      368 369 373 381
Quasi-cocommutative bialgebra      173
Quasi-cocommutative Hopf algebra      173 174 180 182
Quasi-commutative bialgebra      185
Quasi-Hopf algebra      379 381

Quasi-triangular bialgehra      174 198
Quasi-triangular quasi-bialgebra      371 382
QUE      395
Quotient-coalgebra      43
R-matrix      167 169 171 179 194 198 234 311
Real form of a complex Lie algebra      119
Rees algebra      20
Regular link projection      246
Regular tangle projection      260
Reidemeister moves      248 261 271 273
Representation      5
Representation of the tangle category      305
Resolution      447
Restricted dual      71 120 163
Restricted dual of a Hopf algebra      71
Reverse category      337
ribbon      270 313 358
Ribbon algebra      361 365 366 382
Ribbon category      349 360 361 366 410 500
Ribbon functor      504
Riemann's zeta function      468 483
Right comodule      62
Right duality      346 351 366 380
Right unit constraint      282 315 369
Rigidity theorem      426 442
Rnizhnik — Zamolodchikov equations      382 449 455 459 469 479
Root length      406 407
Root of unity      85 90 122 134 139
S      454 456
Scalar product      155
Schur's lemma      20
Semidirect product of groups      202
Semisimple Lie algebra      138 403 407 410 418 427 430 434 442 449 459 460 479 496 499 503
Semisimple module      5 104 144 406
Semisimplicity      143 163
Separated module      388 390
Shuffle      47 68 97 480
Shuffle bialgebra      68
Sign of a permutation      438
Simple module      5 102 103 109 115 118 128 134 136 138 139 154 155 168 234 364 406 410 417 427 431 503
Simple polygonal arc      242
Singular knot      484
Skein module      254
Skein relation      253 486
Skew antipode      55
Skew polynomial ring      22
Source of a morphism      276
Split extension of Lie algebras      422
Square of the antipode      70 85 142 179 382
Square root      399 400 443
Strict tensor, category      282 286 288 295 299 315 319 329 332 337 339 377 380 500
Strict tensor, functor      287 306 312 360
Structure theorem for bimodules over a Hopf algebra      71
Subalgebra      3
Subcategory      276
Subcomodule      62
Submodule      5
Sweedler's Hopf algebra      68 174 196 198 363
Sweedler's sigma notation      43 173 434 461
Symmetric algebra      35 56 95 435 494
Symmetric group      267 454 456 480
Symmetric invariant 2-tensor      405 412 449 455 459 463
Symmetric tensor category      320 337 338 350 371 494
Symmetric tensors      37
Symmetrization of a universal R-matrix      462
Symmetrization, map      98
Symmetry      320
Tangle      257 299
Tangle category      300 306 312 360
Tangle diagram      260 302
Tangle projection      260
Target of a morphism      276
Tensor algebra      34 47 56
Tensor category      282 293 368
Tensor coalgebra      67
Tensor equivalence      288 375
Tensor equivalent categories      288
Tensor functor      287 375
Tensor product of algebras      32
Tensor product of bialgebras      207
Tensor product of coalgebras      42 45 66
Tensor product of comodules      63
Tensor product of linear maps      26
Tensor product of modules      57 98
Tensor product of vector spaces      23 280
Tensor product, algebra      393
Theorem of Milnor and Moore      494
Topological algebra      392 406 424
Topological bialgebra      393 458
Topological braided quasi-bialgebra      393 395 460 469 471
Topological crossed bimodule      395 414
Topological module      394
Topological quasi-bialgebra      393
Topological tensor product      390 410
Topologically free algebra      407
Topologically free module      388 390 400 409 418
Torsion free module      390
Tortile tensor category      366
Trace      21
Trace of an endomorphism      31
TRANSPOSE      343
Transposition      30
Trefoil knot      244 256 313 361
Triangle axiom      282 293 369
Trivial comodule      63
Trivial knot      244 312
Trivial link      244
Trivial module      58 59 98 102
Trivial topological bialgebra      457
Trivial topological braided quasi-bialgebra      394
Twist      349 359 361 366 411 500
Two-variable Jones polynomial      253
Undercrossing      246 260
Unit of a tensor category      282 284 305 316
Universal R-form      185 191 195 197 365
Universal R-matrix      173 175 177 179 198 216 220 230 371 376 393 398 409 412 413 419 458 459
Vassiliev invariant      505
Verma module      130 138
Vertex      242
Weight      101 127
Weyl algebra      18
Whitehead lemmas      117 429
Word      295
Yang — Baxter equation      167 171 178 179 185 191 196 198 234 266 306 311 317 395 418
Yang — Baxter operator      323

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