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| Ïîèñê ïî óêàçàòåëÿì |
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| Chari V., Pressley A. — A Guide to Quantum Groups |
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| Ïðåäìåòíûé óêàçàòåëü |
Lie bialgebra, triangular 54
Lie — Poisson structure 19—20 21
Link invariants 167—168 497
Link invariants from R-matrices 504—510
Link invariants from vertex models 510—517
Linking number 500—501
links 167
Links, equivalent 496
Links, oriented 496
Links, skein related 497
Local algebra 158
Loop representation 542
Lusztig's canonical basis, algebraic construction 486—488
Lusztig's canonical basis, positivity property 487
Lusztig's canonical basis, topological construction 488—490
Lusztig's conjectures 359—361
Manin triples 26—32
Manin triples, infinite-dimensional 28
Markov equivalence 502
Markov moves 502
Markov trace 506
Matched pair 48
Matrix elements 106 116 430
Matrix elements and little q-Jacobi polynomials 466
Matrix elements and little q-Legendre polynomials 467
Matrix elements and q-Bessel functions 470—473
Modified classical Yang — Baxter equation (MCYBE) 55
Modified classical Yang — Baxter equivalent solutions 80
Modular Hopf algebra 517—521
Module 108
Module algebra 109
Module coalgebra 109
monodromy 540
Monodromy theorem 549—550
Monoidal functor 138—139
Monomorphism 137
Non-linear Schroedinger equation 422
Non-restricted integral form 289
Non-restricted specialization 288—296
Non-restricted specialization and conjugacy classes 295—296 342—343 347
Non-restricted specialization and R-matrices 348—351
Non-restricted specialization automorphisms 293—295
Non-restricted specialization centre 290—292
Non-restricted specialization defining relations 289
Non-restricted specialization relation with  290
Non-restricted specialization representations 339—348
Opposite algebra 101
Opposite coalgebra 103
Orbit principle 180 439 442
Ore condition 232 244
Pairing of Hopf algebras 114—115 224—226 461
Partition function 247 249 510
Pentagon axiom 139
Perverse sheaves 490
Peter-Weyl theorem 451
Pluecker relations 448
Poincare — Birkhoff-Witt 199—200 260 282—283 291 298 302 382 394 433
Poisson action 36—37
Poisson algebra 43 177
Poisson algebra deformation 44
Poisson bivector 17
Poisson bracket 16—17
Poisson homogeneous space 22—24
Poisson homogeneous space, Hopf fibration as 23—24
Poisson homogeneous space, symplectic leaves of 38
Poisson manifold 16—21
Poisson manifold, complex 20—21
Poisson map 18
Poisson structure 16—17
Poisson structure, compatible 41
Poisson submanifold 18
Poisson — Hopf algebra 177—178
Poisson — Lie group 21—24 292—293 296
Poisson — Lie group, coboundary 59—68
Poisson — Lie group, compact 35—36
Poisson — Lie group, complex 26
Poisson — Lie group, double 34 37—38 43
Poisson — Lie group, dual 33—34 37—38 296
Poisson — Lie group, factorizable 67
Poisson — Lie group, homomorphism 21
Poisson — Lie group, Lie bialgebra of 26
Poisson — Lie group, subgroup 22
Pontryagin duality 135
Pontryagin product 108
Primitive element 107
Primitive ideal 454
Primitive vector 314 354 383
Principal alcove 362
Pro-finite fundamental group 557
PRODUCT 18
Product, rank of 19 22
Product, second Adler — Gel'fand — Dickii 32
Product, symplectic 18
Product, trivial 18
Product, twisted 42—43
Pseudo-differential operators 31—32
Pseudo-highest weight 396
Pseudo-universal R-matrix 419 423
Pure braid group 144 153 538
Pure sphere braid group 538
q-Bessel function 470
q-Bessel function, addition formula 471
q-Bessel function, Hansel — Lommel orthogonality relation 471
q-binomial coefficient 200 209 301
q-derivative 464
Q-exponential 273
q-factorial 200
q-Hahn polynomial 467
Q-hypergeometric series 430 465 561
q-integral see Jackson integral
q-Jacobi polynomial, big 468—469
q-Jacobi polynomial, little 466—467
q-Legendre polynomial 467
q-number 200
q-spherical function 468—469
QF algebra 176 216—227 234—240 430
QF algebra *-representations 433 437—438 441—442
QF algebra *-structure 431—432
QF algebra admits a faithful representation 438—439
QF algebra and classical function algebra 306 443—444
QF algebra at roots of unity 301 442—445
QF algebra centre 219
QF algebra, differential calculus on 240—246
QF algebra, highest weight representations 227 433—438 441—442
QF algebra, multiparameter 238—240
QF algebra, PBW factorization 433
QF algebra, rational form 280—281
QF algebra, twisted 439—442
QFSH algebra 190 267—268
Quantization of co-Poisson — Hopf algebras 180
Quantization of Lie bialgebras 180—189
Quantization of Poisson — Hopf algebras 179
Quantization of Poisson — Lie groups 179
Quantization of quasi-Hopf algebras 537
Quantization, deformation 46—47
Quantization, homogeneous 375—376
Quantization, Moyal 46—47 183—187
Quantization, multiparameter 212—213 238—240
Quantization, non-standard 206—207
Quantization, R-matrix 187 222—223 228—234
Quantization, standard 195 208 234—235
Quantization, Weyl 44—45
Quantized algebra of continuous functions 451—452
Quantized algebra of continuous functions, vanishing at infinity 461—462
Quantized function algebra see QF algebra
Quantum  192—206 216—227
Quantum  and little g-Jacobi polynomials 466—467
Quantum , algebra structure 196
Quantum , automorphisms 309
Quantum , basis 199 220—222 226
| Quantum , centre 285 291—292 321—323
Quantum , matrix elements 466
Quantum , quantum Weyl group 262—263
Quantum , quasitriangular structure 201—203
Quantum , real forms 309—311
Quantum , representations 203—206 330—331 343—344
Quantum , tilting modules 364—366
Quantum , universal R-matrix 201 263—265
Quantum , Weyl modules 355—356
Quantum affine algebra 392—394
Quantum affine algebra, PBW basis 394
Quantum affine algebra, pseudotriangular structure 403 423—425
Quantum Casimir element 196 285 291—292 323
Quantum Clebsch — Gordan coefficient 205 467
Quantum coadjoint action 293—296
Quantum coadjoint action and conjugacy classes 295—296
Quantum coordinate ring see QF algebra
Quantum determinant 219 220 231—233 236
Quantum dimension 122—123 126 365—366 371
Quantum double 127—129 132
Quantum euclidean group 459—462 469—470
Quantum euclidean group representations 462—463
Quantum euclidean group, automorphisms 463
Quantum euclidean group, Haar integral 463—465
Quantum field theory 157—160
Quantum flag manifolds 447—448
Quantum G-space 445—447
Quantum Kac — Moody algebras 207—213
Quantum Kac — Moody algebras, automorphisms 309
Quantum Kac — Moody algebras, centre 212 284—285 290—293 321—324
Quantum Kac — Moody algebras, geometric realization 285—288 308—309
Quantum Kac — Moody algebras, real forms 309—311
Quantum Kac — Moody algebras, representations 313—331
Quantum loop algebras 396
Quantum loop algebras, relation with Yangians 403
Quantum loop algebras, representations 394—403
Quantum orthogonal group 236—238
Quantum plane 217—218 228 240—241
Quantum projective space 451
Quantum R-matrix 133 205 276—277
Quantum R-matrix, elliptic 427
Quantum R-matrix, Frobenius 231
Quantum R-matrix, Hecke 232
Quantum R-matrix, rational 380 419—423
Quantum R-matrix, singularities 425
Quantum R-matrix, strange 230
Quantum R-matrix, trigonometric 424
Quantum Schubert variety 448
Quantum Schur orthogonality relations 457—458
Quantum Serre relation 209
Quantum special linear group 235—236
Quantum spheres 448—451 467—469
Quantum symplectic group 236—238
Quantum torus 442
Quantum trace 122—123 126—127 365—366 370
Quantum Weyl group 262—266 439
Quantum Weyl group and central elements 265
Quantum Weyl group and universal R-matrix 263—265
Quantum Weyl group for quantum affine algebras 424
Quantum Yang — Baxter equation (QYBE) 67 124—125 187 203 229 250
Quantum Yang — Baxter equation (QYBE) and braid groups 504—505
Quantum Yang — Baxter equation (QYBE) and intertwiners 348—351
Quantum Yang — Baxter equation (QYBE) with spectral parameters 250 348—351 380 419—425 511
Quantum Yang — Baxter equation (QYBE), space of solutions of 233—234
Quasi-bialgebra 529
Quasi-bialgebra, quasitriangular 531
Quasi-bialgebra, triangular 531
Quasi-Frobenius Lie algebra 84
Quasi-Hopf algebra 130—131 529
Quasi-Hopf algebra, quasitriangular 531
Quasi-Hopf algebra, triangular 531
Quasi-Hopf QUE algebra 534—537
Quasi-Hopf QUE algebra, quasitriangular 536
Quasi-Lie bialgebra 536
Quasi-modular Hopf algebra 521
Quasi-Poisson — Lie group 48
Quasi-quantum Yang — Baxter equation 531
QUE algebra 176 187—192
QUE algebra, coboundary 188
QUE algebra, cocommutative 187—188
QUE algebra, quasitriangular 188
QUE algebra, rational form 280—281
QUE algebra, triangular 188
QUE double 190 266—267 270
QUE dual 190 267 268—270
quiver 307 488—490
Rational form 280—281
Rational form and R-matrices 327—329
Rational form, adjoint 281
Rational form, simply-connected 281
Real form 117—119
Real form, compact 431
Real form, equivalent 117
Reconstruction theorem 147—149
Reduced decomposition 565
Reduced decomposition, adapted 488
Regular dominant weight 433
Regular isotopy 500 512
Reidemeister moves 496—497
Representation and symplectic leaves 180 439 442 454
Representation, adjoint 110
Representation, characters 315
Representation, completely reducible 391
Representation, corresponding to a Schubert cell 435 441 448
Representation, cyclic 344—348
Representation, dual 110—111
Representation, faithful 438—439
Representation, highest weight 314 324 433
Representation, integrable 314 492 556 566
Representation, physical 158
Representation, pseudo-highest weight 396
Representation, regular 110
Representation, restricted 359
Representation, tame 415
Representation, tensor products 110
Representation, trivial 110
Representation, type 314 394 401
Representation, unitarizable 433
Representation, unitary 118 329—331 433
Representative functions 106 116
Restricted enveloping algebra 304 360
Restricted integral form 296—297
Restricted integral form of a representation 316
Restricted integral form, basis 298
Restricted integral form, generators and relations 299—300
Restricted representation 359
Restricted specialization 300
Restricted specialization and affine Lie algebras 360—361
Restricted specialization, centre 300
Restricted specialization, representations 351—361
Ribbon Hopf algebra 125—127 133 161 276 517
Ribbon Hopf algebra, central elements 168—169
Ribbon tangle 146—147 502
Ribbon tangle closure 164—165
Ribbon tangle, coloured 147
Ribbon tangle, directed 146—147
Ribbon tangle, isotopy invariants 161—166
Right dual 111 122
Rigidity theorems 176—177 212
Robinson — Schensted correspondence 478
Root 563
Root space 564
Root vector 259 282 565
Rotation number 501
Schouten bracket 17
Schubert cell 41 435 441 448
Segment 402
Short exact sequence 137
Simple object 137
Simple reflection 564
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