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

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Предметный указатель

Quantum group, $GL_q(N;\mathbb{R})$       316
Quantum group,       320
Quantum group,       325
Quantum group,       325
Quantum group, $O_q(N;\mathbb{R})$       326
Quantum group, $O_q(N;\nu)$       326
Quantum group,       100
Quantum group, $SL_q(2,\mathbb{R})$       102
Quantum group,       315
Quantum group, $SL_q(N;\mathbb{R})$       316
Quantum group,       323
Quantum group, $SO_q(N;\mathbb{R})$       326
Quantum group,       320
Quantum group, $Sp_q(N;\mathbb{R})$       325
Quantum group, $Sp_q(N;\nu)$       326
Quantum group,       102
Quantum group,       102
Quantum group, , C*-algebra      118
Quantum group,       317
Quantum group, $SU_q(N;\nu)$       317
Quantum group,       326
Quantum group,       316
Quantum group, compact      317 326
Quantum group, inhomogeneous      387 392
Quantum homogeneous space      442 451
Quantum hyperboloid      472
Quantum Killing form      189
Quantum Lie algebra      501
Quantum Lie derivative      515
Quantum matrix space      98 304 310
Quantum orthogonal sphere      322
Quantum plane      101
Quantum projective space      453
Quantum space      32 436
Quantum space, isomorphism of      125
Quantum space, left      32 438
Quantum space, right      32 436
Quantum sphere      449
Quantum spherical function      129
Quantum subgroup      105 323
Quantum symmetric subspace      273
Quantum symplectic space      324
Quantum tangent space      494
Quantum trace      206
Quantum unitary group      316
Quantum vector space      308 310
Quantum Weyl algebra      469
Quantum Yang — Baxter equation      61 245 247 297 333 337
Quantum zonal spherical function      450 453
Quasi-Hopf algebra      358
R Matrix      61 247 264
R Matrix of a vector representation      270
R Matrix, universal      61 243 254 259 261
Racah coefficients      83
Real form      21 58 102 172 316 325
Real form, compact      172
Realification      363
Reflection equation      346 368
Representation      27
Representation of class 1      217
Representation of type 1      62 178 213
Representation with highest weight      61 70 141 177 199
Representation with lowest weight      70 141
Representation, adjoint      35
Representation, character of      203
Representation, completely reducible      28 200

Representation, conjugate      35
Representation, cyclic      69 145 234
Representation, Fock      149
Representation, intertwiner of      28
Representation, irreducible      28
Representation, rational      31 484
Representation, self-dual      271
Representation, semicyclic      70 145
Representation, tensor product of      28 69
Representation, TV-finite      140
Representation, weight      64 177
Root      157
Root vector      175
Root, negative      158
Root, positive      158
Root, simple      158
Root, subspace      157
Rosso form      188 257
Schur orthogonality relations      419
Serre relations      160
Shuffle      19
Skew-copairing      358
Skew-pairing      250
Skew-pairing, invertible      250
Subcoalgebra      9
Sweedler notation      10 31
Sweedler's Hopf algebra      19 244 337
Symmetric algebra      19
Symmetric algebra of a bicovariant bimodule      490
Tensor algebra of a bicovariant bimodule      485
Tensor algebra of a vector space      8 19 24
Tensor operator      93 219
Tensor product of bicovariant bimodules      481
Tensor product of corepresentations      32 397
Tensor product of representations      28 69
Tensor product, algebra      8
Tensor product, coalgebra      9
Theorem, Poincare — Birkhoff — Witt      160 176
Theorem, Wigner — Eckart      93 219
Transfer matrix      295
Transmutation      375
Triangular condition      83
Universal enveloping algebra      18 160
Universal R-form      331
Universal r-form, factorizable      372
Universal r-form, inverse real      336 341
Universal r-form, real      336 340
Universal r-form, regular      366
Universal R-matrix      61 243 254 259 261
Vector representation      210 267
Vector weight      64
Vector weight, highest      64 177
Verma module      179
Weight      64 177
Weight space      64 177
Weight vector      64
Weight, highest      64 177
Weight, multiplicity of      177 203
Weight, representation      64 177
Weyl group      158
Wigner — Eckart theorem      93 219
Yang — Baxter equation, quantum      61 245
Yang — Baxter equation, rational      297
Yang — Baxter equation, trigonometric      297
Yetter — Drinfeld condition      478
Yetter — Drinfeld module      478 484
Young diagram      289

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