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Chari V., Pressley A. Ч A Guide to Quantum Groups
Chari V., Pressley A. Ч A Guide to Quantum Groups



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Ќазвание: A Guide to Quantum Groups

јвторы: Chari V., Pressley A.

јннотаци€:

Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. This book gives a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Researchers in mathematics and theoretical physics will enjoy this book.


язык: en

–убрика: ћатематика/јлгебра/ вантовые группы/

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

ed2k: ed2k stats

√од издани€: 1994

 оличество страниц: 667

ƒобавлена в каталог: 26.03.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
*-homomorphism      117
*-representation      433 437Ч439 441Ч442
3-manifold invariants      522Ч525
Absolute Galois group      557Ч560
Admissible      80 92 482
Affiliated element      462
Affine Hecke algebra      403
Affine Hecke algebra, relation with p-adic groups      404
Affine Hecke algebra, representations      405Ч408 410Ч413
Affine Lie algebra      58 541Ч543 550Ч556 565Ч566
Alexander polynomial      498 500
Algebra      101Ч102
Algebra, deformation      43
Algebra, opposite      101
Ambient isotopy      496 514
Angle 1-form      501
Antipode      103 529
Antipode, square of      190Ч192
arrow      482
Associativity constraint      139
Baker Ч Campbell Ч Hausdorff formula      46 182 185Ч186
Big cell      294
Birkhoff factorization theorem      96
Birman Ч Murakami Ч Wenzl algebra      334 526
Boltzmann weight      247 351 510
BOND      246
Braid      142Ч144
Braid closure      501
Braid group      143Ч144 153 256
Braid group and configuration spaces      538
Braid group, action      257 282 336
Brauer Ч Frobenius Ч Schur duality      see Frobenius Ч Schur duality
Bruhat decomposition      39 41
Bruhat ordering      360 405 565
Burau representation      505
C* -completion      451Ч452
C* -completion, type of      454
Capelli identity      426
Cartan matrix      562
Cartan matrix, extended      565Ч566
Casimir element      196 275Ч276
Category, abelian      136Ч137 307
Category, additive      136Ч137
Category, balanced      154
Category, braided monoidal      153
Category, essentially small      148
Category, k-linear      137
Category, monoidal      138Ч147 530
Category, quasitensor      152Ч153 329 359 370 531 555 559Ч560
Category, rigid      139Ч140 530 555
Category, semisimple      137 391 556
Category, small      148
Category, strict      139
Category, tensor      149Ч152 531
Central character      290 315 340
Central elements      122 124 168Ч169 284 321Ч323
CHARACTER      317 325Ч326 353Ч354 361 363
Characteristic p      296 304Ч306 358Ч361 555Ч556
Classical limit of a QF algebra      179
Classical limit of a quasi-Hopf QUE algebra      536Ч537
Classical limit of a QUE algebra      180Ч182
Classical r-matrix      54 181Ч182 183Ч184
Classical r-matrix and 2-cocycles      62Ч63
Classical r-matrix and integrable systems      71Ч77
Classical r-matrix, non-degenerate      62 87
Classical Yang Ч Baxter equation (CYBE)      54 125 182 187
Classical Yang Ч Baxter equation (CYBE) and Lie bialgebras      51
Classical Yang Ч Baxter equation (CYBE) with spectral parameters      87
Classical Yang Ч Baxter equation (CYBE), class of solution of      96
Classical Yang Ч Baxter equation (CYBE), equivalent solutions of      80 84 88
Classical Yang Ч Baxter equation (CYBE), modified      55
Classical Yang Ч Baxter equation (CYBE), solutions of      80Ч98
Clebsch Ч Gordan decomposition      204 326
Co-Jacobi identity      178
Co-Leibniz identity      178
Co-Poisson algebra      178
Co-Poisson Hopf algebra      178
Coadjoint orbits      20 40Ч41
Coalgebra      102Ч103
Coassociativity      102
Coassociator      529
Coboundary      51 84 174
Cochain      173
Cocommutator      25 535
Cocycle      25 62 174 533
Cohomology of Hopf algebras      173Ч177
Cohomology of Hopf algebras, rigidity theorems for      176Ч177 212
Cokernel      137
Comodule      108
Comodule algebra      109
Comodule coalgebra      109
Compact matrix pseudogroup      see compact matrix quantum group
Compact matrix quantum group      453Ч454
Compact matrix quantum group, Haar integral      454Ч458
Complete integrability      68Ч69
Complete reducibility      318Ч319 324Ч325
Comultiplication      102
Configuration spaces      537Ч538 558
Conformal field theory      159 371Ч372
Conformal field theory, orbifold      534
Conformal weight      542
Conserved quantities      69
Conserved quantities in involution      69
Continued fraction      331
Continuous series      331
Contravariant form      320
Convolution product      104
Core      146
Corepresentation      110 141
Corepresentation, regular      110
Corepresentation, unitary      118
Coxeter automorphism      91
Coxeter element      489 565
Coxeter number      92 489 565
Crystal basis      478Ч486
Crystal basis, global      480Ч486
Crystal graph      484
De Rham complex of quantum $GL_m$      244Ч245
De Rham complex of quantum $m \Times m$ matrices      242Ч243
De Rham complex of quantum plane      240Ч241
De Rham complex, homology of      243Ч244
Deformation of algebras      43
Deformation of bialgebras      171
Deformation of Hopf algebras      171
Deformation of Poisson algebras      44
Deformation, (mod $h^n$)      172
Deformation, quantization      44 46Ч47
Degenerate affine Hecke algebra      405
Derivation      190Ч192
Determinant formula      321 327
Diagonal module      342
Diagram automorphism      309
Differential graded algebra      242
Direct sum      136
Directed tangle      145
Discrete series      330
Discriminant      340Ч341
Dressing action      37Ч38
Dressing action and symplectic leaves      38Ч41
Dressing transformation      37Ч38
Dual basis lemma      141
Dual Coxeter number      564
Dual object      139
Dual object functor      140
Dynkin diagram      92 562
Dynkin graph      307
Eight vertex model      253
Elliptic solutions of the CYBE      90Ч91
Elliptic solutions of the QYBE      427
Enhanced quantum Yang Ч Baxter operator      506
Epimorphism      137
Equivalence of deformations      171
Equivalence of solutions of the CYBE      80 84 8?
Euclidean group      459
Evaluation homomorphism for affine Hecke algebras      407
Evaluation homomorphism for quantum loop algebras      399Ч401
Evaluation homomorphism for Yangians      386Ч387
Evaluation representations of affine Hecke algebras      407
Evaluation representations of quantum loop algebras      399Ч403
Evaluation representations of Yangians      386Ч391
Exterior algebra      107Ч108
Fateev Ч Zamolodchikov model      351
Fibonacci sequence      331
Framing      502
Frobenius Lie algebra      84
Frobenius map      305Ч306 357 359
Frobenius Ч Schur duality for $U_{\epsilon}(g)$      334Ч335 408Ч410
Frobenius Ч Schur duality for quantum affine algebras      410Ч413
Frobenius Ч Schur duality for Yangians      413Ч414
Frobenius Ч Schur duality, classical      332
Fuchsian differential equations      544
Functor, exact      148
Functor, faithful      148
Functor, monoidal      138Ч139
Functor, tensor      150
Fundamental reflection      see simple reflection
Fundamental representations of quantum loop algebras      399
Fundamental representations of Yangians      384 387Ч388
Fundamental weight      564
Fusion matrices      155
Fusion ring      155 159 160 371
Fusion rules      154Ч157 160
Fusion tensor product      371 552Ч555
Gabriel's theorem      307Ч308 489
Gel'fand Ч Naimark Ч Segal state      439
Gel'fand Ч Tsetlin basis      476Ч478
Generalized Cartan matrix      562
Graphs, admissible      482
Graphs, coloured oriented      482
Graphs, crystal      484
Graphs, tensor products of      483Ч486
Grothendieck group      137Ч138
Grothendieck ring      139 156
Grothendieck Ч Teichmuller group      558Ч559
Grothendieck Ч Teichmuller group and quasi-Hopf algebras      559Ч560
Group algebra      105 112 175
Group cohomology      533Ч534
Group-like      106 193
H-adic topology      105
Haar integral      see integral invariant
Hamiltonian      68Ч69
Hamiltonian vector field      17
Harish Chandra homomorphism      284 290 321Ч324
Harish Chandra homomorphism and quantum coadjoint action      296
Harish Chandra's theorem      285 290
Hecke algebra      332Ч336 404 476
Hecke algebra, representations      405Ч406
Heisenberg ferromagnet      see XXX model
Heisenberg group      45 218
Heisenberg Lie algebra      44Ч45 176 186
Hermitian symmetric space      41
Highest weight      314 354 383 434 441
Highest weight module      314 324 354 542
Highest weight module for QF algebras      434 441
Highest weight module for Yangians      383
Highest weight vector      314 383
Hilbert space tensor product      415
Hochschild cohomology      174 254
Homfly polynomial      497Ч498 509 517
HOMFLY polynomial for trefoil knot      498Ч499
Hopf algebra      103Ч105
Hopf algebra, *-structure      117Ч119 309Ч311 329 431Ч432
Hopf algebra, almost cocommutative      119
Hopf algebra, coboundary      123
Hopf algebra, cocommutative      102
Hopf algebra, cohomology      173Ч177
Hopf algebra, deformations      171
Hopf algebra, dual      111Ч115 131Ч132 223Ч226 234Ч235
Hopf algebra, Graded      105
Hopf algebra, integral on      115Ч116 132
Hopf algebra, quasitriangular      123 129Ч130
Hopf algebra, representations      108Ч112
Hopf algebra, ribbon      125 133
Hopf algebra, topological      105 114 123
Hopf algebra, triangular      123 150Ч151
Hopf ideal      103Ч104
Hopf link      165Ч166
Hopf's theorem      108
Hyperalgebra      304 358 359Ч360
Identity object      138
Infinite-dimensional orthogonal group      414Ч417
Infinitesimal deformation      172
integral      115Ч116
Integral form, non-restricted      289
Integral form, restricted      297
Intersection cohomology      489
Intertwiner      151 348Ч351 542
Invariant      115
Invariant bilinear form      563
Invariant bilinear form, orthogonality properties      564
Invariant differential form      245Ч246
Invariant, non-central      456
Invariant, normalized      115
Ising model      371Ч372
Jackson integral      457 467
Jacobi identity      17
Jacobson topology      454
Jets      391
Jones polynomial      168 498 500
Kac Ч Moody algebra      562
Kashiwara's tensor product algorithm      485Ч486
Kauffman polynomial      499 500 510 517
Kazhdan Ч Lusztig element      406
Kazhdan Ч Lusztig polynomial      360
Kazhdan Ч Lusztig tensor product      552Ч555
Kernel      137
Kink      501
Kirby move      503 522Ч525
Kirby move, special      503
Kirillov Ч Kostant principle      see orbit principle
Knizhnik Ч Zamolodchikov equation      539Ч541
Knizhnik Ч Zamolodchikov equation and hyperplane complements      561
Knizhnik Ч Zamolodchikov equation and m-point functions      542Ч543
Knizhnik Ч Zamolodchikov equation and quantization      543Ч549 555
Knot      496
Kohno Ч Drinfel'd monodromy theorem      549Ч550
Lattice model, exactly solvable      247
Lattice model, integrable      246Ч253
Lax pair      69Ч71 73 76
Left dual      111 122
Leibniz identity      17
Length      565
Level      408Ч409
Level for affine Lie algebras      566
Lie bialgebra      24Ч33
Lie bialgebra, automorphism      32
Lie bialgebra, coboundary      50Ч59
Lie bialgebra, cocommutator of      25
Lie bialgebra, derivation      32Ч33
Lie bialgebra, double      34Ч35 58Ч59
Lie bialgebra, dual      33Ч34
Lie bialgebra, factorizable      67
Lie bialgebra, homomorphism      25
Lie bialgebra, ideal      25
Lie bialgebra, opposite      25
Lie bialgebra, pseudotriangular      56
Lie bialgebra, quasitriangular      54
Lie bialgebra, quotient      25
Lie bialgebra, standard      29Ч30 34Ч36 55Ч56 59 81 93
Lie bialgebra, tangent      26
1 2 3
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