Klimyk A., Schmudgen K. — Quantum Groups and Their Representations :: Электронная библиотека попечительского совета мехмата МГУ

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Klimyk A., Schmudgen K. — Quantum Groups and Their Representations

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Название: Quantum Groups and Their Representations

Авторы: Klimyk A., Schmudgen K.

Аннотация:

This book provides a detailed treatment of the most important quantum groups and q-deformed algebras, as well as their representations and co-representations. Many applications in mathematical and theoretical physics are presented, including topics such as q-oscillator algebras, quantum vector spaces, and noncommutative differential calculus.

Язык:

Рубрика: Математика/Алгебра/Квантовые группы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 552

Добавлена в каталог: 26.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$4D\pm$ -Calculus      504
$\mathbb{N}_0$ -Graded super Hopf algebra      23 489 511 512
*-algebra      20
*-Algebra, Hopf      20
*-Algebra, left comodule      33
*-Algebra, right comodule      33
*-Bialgebra      20
*-Coalgebra      20
*-Quantum space      33
*-representation      28 123 420
*-Vector space      20
2-cocycle      354 357
2-Cocycle, cohomologous      355
2-Cocycle, counital      357
2-Cocycle, invertible      357
2-Cocycle, left      354
2-Cocycle, right      354
3D-Calculus      497 510
Action, adjoint      34 181
Action, left      27 34
Action, right      27 34
Algebra      7
Algebra, associative      6
Algebra, Birman — Wenzl — Murakami      293
Algebra, crossed product      349 383
Algebra, Drinfeld — Jimbo      163
Algebra, free      8
Algebra, h-adic      26
Algebra, Hecke      293
Algebra, homomorphism of      7
Algebra, Hopf      4
Algebra, involution of      20
Algebra, left comodule      33
Algebra, left module      33
Algebra, multiplication of      7
Algebra, opposite      8
Algebra, right comodule      32
Algebra, right module      33
Algebra, unit of      7
Algebra, universal enveloping      18 160
Antipode      13
Antipode, inverse of      20 247 334
Antipode, Order of      15
Antipode, polar decomposition of      426
Antipode, square of      15 164 247 334
Bargmann — Fock realization      151 153
Basis at q = 0      226
Baxterization      296
Bialgebra      11
Bialgebra, braided      373
Bialgebra, comatched pair of      362
Bialgebra, coquasitriangular      331
Bialgebra, cotriangular      331
Bialgebra, double crossed coproduct      363
Bialgebra, double crossed product      360
Bialgebra, dual      22
Bialgebra, FRT      304
Bialgebra, homomorphism of      12
Bialgebra, matched pair of      359
Bialgebra, quasitriangular      243
Bialgebra, triangular      243
Bicharacter      24 336
Biedenharn — Elliott identity      88
Biideal      12
Bimodule      28
Bimodule, bicovariant      477
Bimodule, bicovariant, braiding of      481
Bimodule, bicovariant, homomorphism of      481
Bimodule, bicovariant, tensor product of      481
Bimodule, left-covariant      473
Bimodule, right-covariant      477
Birman — Wenzl — Murakami algebra      293
Bosonization      383
Braid group      173 486
Braid relation      247 482
Braided Hopf algebra      373 376
Braided line      374
Braided matrix algebra      368
Braided product      373 376
Braided product algebra      378
Braided tensor category      378
Braided vector algebra      382
Braiding      373 378 481
Brauer — Schur — Weyl duality      291
Cartan matrix      159
Cartan matrix, symmetrized      159
Cartan subalgebra      157
Category      376
Category, algebra in      378
Category, tensor, monoidal      377
Category, tensor, monoidal, braided      378
CHARACTER      422
Clebsch — Gordan coefficient      74 211
Clebsch — Gordan coefficient, reduced      219
Coaction, adjoint      34
Coaction, left      29 34
Coaction, right      29 34
Coalgebra      9
Coalgebra, cocommutative      9
Coalgebra, comultiplication of      9
Coalgebra, coopposite      9
Coalgebra, cosimple      398
Coalgebra, dual      22
Coalgebra, homomorphism of      9
Coalgebra, twisting of      357
Coassociativity      9
Coboundary      355
Coefficient, Clebsch — Gordan      74 211
Coefficient, coalgebra      400
Coefficient, q-binomial      39
Coefficient, Racah      83
Coherent state      152
Coideal      9
Comodule      29
Comodule, algebra      32
Comodule, coalgebra      352
Comodule, left      30
Comodule, morphism of      30
Comodule, right      30
Compact quantum group, algebra      415
Compact quantum group, C*-algebra      429 434
Compact quantum group, matrix algebra      415
Comultiplication      9
Contraction of a differential form      516
Convolution product      10
Coordinate algebra      98 100 304 308 310 315 320 324 388 449
Coproduct      9
Coproduct, smash      350
Corepresentation      29 395 429
Corepresentation, character of      406
Corepresentation, conjugate      398
Corepresentation, contragredient      398
Corepresentation, equivalent      30
Corepresentation, fundamental      305
Corepresentation, intertwiner      28 397
Corepresentation, irreducible      30 398
Corepresentation, isomorphism of      28
Corepresentation, matrix      30 397
Corepresentation, tensor product of      32 397
Corepresentation, trivial      29
Corepresentation, unitarizable      402
Corepresentation, unitary      30 114 402
Counit      9
Crossed coproduct coalgebra      353 382
Crossed product algebra      349 383
Crystal basis      227 231
Crystal basis, global      230 231
Diamond lemma      103
Differential *-calculus      462
Differential calculus      461

Differential calculus, first order      457
Differential calculus, left-covariant      463
Differential calculus, quotient      461
Differential calculus, universal      463 508
Differential calculus, universal of a first order      463 509
Differential envelope      463 508
Differential graded algebra      461
Differential Hopf algebra      511
Differential ideal      461
Double crossed coproduct bialgebra      363
Double crossed product bialgebra      360
Drinfeld — Jimbo algebra      163
Drinfeld — Jimbo algebra, center of      192 194
Drinfeld — Jimbo algebra, h-adic      166
Drinfeld — Jimbo algebra, rational      165
Dual pairing      16 21 120 327
Dual pairing, nondegenerate      17 120 410 440
Element, biinvariant      105 443 451
Element, canonical      256
Element, group-like      12
Element, invariant      30 324 443 451
Element, locally finite      181
Element, primitive      12
Element, twisted primitive      129
Euler derivation      469
Exterior algebra of a bicovariant bimodule      488
Exterior algebra of the quantum Euclidean space      320
Exterior algebra of the quantum plane      102
Exterior algebra of the quantum symplectic space      324
Exterior algebra of the quantum vector space      310
First order differential calculus      457
First order differential calculus, bicovariant      499
First order differential calculus, bicovariant, classification of      527
First order differential calculus, bicovariant, construction of      517 521
First order differential calculus, bicovariant, quantum Lie algebra of      501
First order differential calculus, left-covariant      459 491
First order differential calculus, left-covariant, dimension of      495
First order differential calculus, left-covariant, quantum tangent space of      494
First order differential calculus, left-covariant, quotient      493
First order differential calculus, left-covariant, right ideal associated with      493
First order differential calculus, left-covariant, right-covariant      464 498
First order differential calculus, universal      463 492
Flip operator      6
Fock representation      149
Fourier transform on       117
FRT bialgebra      304
Function, basic hypergeometric      41
Function, coordinate      5
Function, q-exponential      47
Function, q-gamma      48
Function, q-trigonometrical      47
Function, spherical      129
Fundamental matrix      302
Gel'fand — Tsetlin basis      214
GNS representation      421
Group algebra      19
h-Adic algebra      26
h-Adic Drinfeld — Jimbo algebra      166
h-Adic Hopf algebra      26
H-adic topology      25
Haar functional      112 404
Haar functional, faithfulness      419
Haar state      114 420 431
Harish — Chandra homomorphism      193
Hecke algebra      293
Heisenberg double      351
Heisenberg representation      350
Hexagon relation      90
Hopf *-algebra      20
Hopf algebra      4 13
Hopf algebra, $\mathbb{N}_0$ -graded super      23
Hopf algebra, braided      373 376
Hopf algebra, coquasitriangular      331
Hopf algebra, cosemisimple      402
Hopf algebra, deformation of      26
Hopf algebra, differential      511
Hopf algebra, dual      22
Hopf algebra, factorizable      372
Hopf algebra, h-adic      26 60
Hopf algebra, homomorphism of      16
Hopf algebra, quasi-cocommutative      248
Hopf algebra, quasitriangular      61 243
Hopf algebra, super      24
Hopf algebra, triangular      243
Hopf bimodule      477
Hopf ideal      16
Intertwining operator      28 30
Jordan — Schwinger realization      138
KMS condition      424
Kostant partition funtion      176
L-functional      276 284 342 345
L-operator      275
Leibniz rule      458
Leibniz rule, graded      461
Leibniz rule, twisted      506 515 516
Linear form, -invariant      335
Linear form, dominant      179
Linear form, integral      179
Linear functional, central      422
Linear functional, invariant      111 187
Linear functional, left-invariant      403
Linear functional, right-invariant      128 403
Matrix coefficient, element      30 74 276 396
Maurer — Cartan formula      507
Modular automorphism group      425
Module      27
Module algebra      33 349
Module coalgebra      33
Module, isomorphism of      28
Module, left      27
Module, morphism of      28
Module, right      27
Module, simple      28
Module, Verma      178
Module, Yetter — Drinfeld      478
Multiplicative unitary      427
Multiplicity of weight      177 203
Partial derivative      466
Partition function      176 295
Pentagon equation      427
Peter — Weyl decomposition      110 404 410 439
Poincare — Birkhoff — Witt theorem      160 176
Polynomials, big q-Jacobi      52
Polynomials, little q-Jacobi      51
Polynomials, q-Hermite      50
Product, braided      373 376
Product, covariantized      368
Product, smash      350
q-binomial coefficients      39
q-Coherent state      152
Q-differentiation      44
q-factorial      37
q-integral      46
q-number      37
q-Oscillator algebra      133
q-Oscillator algebra, symmetric      134
Quantum 2-sphere      126
Quantum algebra      53
Quantum antisymmetric subspace      273
Quantum antisymmetrizer      488
Quantum Borel subgroup      436
Quantum Casimir element      54 190 248
Quantum codouble      359 363
Quantum determinant      99 312
Quantum dimension      207 442
Quantum double      252 356 361 483
Quantum Euclidean space      320
Quantum Gel'fand pair      446 450
Quantum Gel'fand pair, infinitesimal      454
Quantum group,       315

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