Quantum groups and their representations:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1997
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| Series: | Texts and monographs in physics
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| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007834260&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverz. S. 529 - 544 |
| Physical Description: | XIX, 552 S. |
| ISBN: | 3540634525 |
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| 100 | 1 | |a Klimyk, Anatolij U. |d 1939-2008 |e Verfasser |0 (DE-588)115774580 |4 aut | |
| 245 | 1 | 0 | |a Quantum groups and their representations |c Anatoli Klimyk ; Konrad Schmüdgen |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
| 300 | |a XIX, 552 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Texts and monographs in physics | |
| 500 | |a Literaturverz. S. 529 - 544 | ||
| 650 | 4 | |a Groupes quantiques | |
| 650 | 7 | |a Groupes quantiques |2 ram | |
| 650 | 7 | |a Représentations de groupe |2 ram | |
| 650 | 4 | |a Représentations de groupes | |
| 650 | 4 | |a Quantum groups | |
| 650 | 4 | |a Representations of quantum groups | |
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| adam_text | Table of Contents
Part I. An Introduction to Quantum Groups
1. Hopf Algebras 3
1.1 Prolog: Examples of Hopf Algebras of Functions on Groups . . 3
1.2 Coalgebras, Bialgebras and Hopf Algebras 6
1.2.1 Algebras 6
1.2.2 Coalgebras 8
1.2.3 Bialgebras 11
1.2.4 Hopf Algebras 13
1.2.5* Dual Pairings of Hopf Algebras 16
1.2.6 Examples of Hopf Algebras 18
1.2.7 ^ Structures 20
1.2.8* The Dual Hopf Algebra A° 22
1.2.9* Super Hopf Algebras 23
1.2.10*/i Adic Hopf Algebras 25
1.3 Modules and Comodules of Hopf Algebras 27
1.3.1 Modules and Representations 27
1.3.2 Comodules and Corepresentations 29
1.3.3 Comodule Algebras and Related Concepts 32
1.3.4* Adjoint Actions and Coactions of Hopf Algebras 34
1.3.5* Corepresentations and Representations
of Dually Paired Coalgebras and Algebras 35
1.4 Notes 36
2. g Calculus 37
2.1 Main Notions on g Calculus 37
2.1.1 q Numbers and q Factorials 37
2.1.2 g Binomial Coefficients 39
2.1.3 Basic Hypergeometric Functions 40
2.1.4 The Function i fQ{a; q,z) 41
2.1.5 The Basic Hypergeometric Function 2fi 42
2.1.6 Transformation Formulas for 3 p2 and 4v?3 43
2.1.7 g Analog of the Binomial Theorem 44
2.2 ^ Differentiation and ^ Integration 44
2.2.1 ^ Differentiation 44
X Table of Contents
2.2.2 g Integral 46
2.2.3 g Analog of the Exponential Function 47
2.2.4 g Analog of the Gamma Function 48
2.3 ^ Orthogonal Polynomials 49
2.3.1 Jacobi Matrices and Orthogonal Polynomials 49
2.3.2 q Hermite Polynomials 50
2.3.3 Little g Jacobi Polynomials 51
2.3.4 Big g Jacobi Polynomials 52
2.4 Notes 52
3. The Quantum Algebra t/a(sl2) and Its Representations ... 53
3.1 The Quantum Algebras Uq(sl2) and Uh(sl2) 53
3.1.1 The Algebra t/,(sl2) 53
3.1.2 The Hopf Algebra Uq(sl2) 55
3.1.3 The Classical Limit of the Hopf Algebra Uq(sl2) 57
3.1.4 Real Forms of the Quantum Algebra Uq(s 2) 58
3.1.5 The /i Adic Hopf Algebra Uh(sl2) 60
3.2 Finite Dimensional Representations of Uq(s 2)
for q not a Root of Unity 61
3.2.1 The Representations Tw 61
3.2.2 Weight Representations and Complete Reducibility ... 63
3.2.3 Finite Dimensional Representations of t/q(s 2)
and Uh(s 2) 65
3.3 Representations of Uq(s 2) for q a Root of Unity 66
3.3.1 The Center of Uq(sl2) 66
3.3.2 Representations of Uq(sl2) 67
3.3.3 Representations of UTqes(sl2) 71
3.4 Tensor Products of Representations.
Clebsch Gordan Coefficients 72
3.4.1 Tensor Products of Representations Ti 72
3.4.2 Clebsch Gordan Coefficients 74
3.4.3 Other Expressions for Clebsch Gordan Coefficients ... 78
3.4.4 Symmetries of Clebsch Gordan Coefficients 81
3.5 Racah Coefficients and 6j Symbols of Uq(su2) 82
3.5.1 Definition of the Racah Coefficients 82
3.5.2 Relations Between Racah
and Clebsch Gordan Coefficients 84
3.5.3 Symmetry Relations 84
3.5.4 Calculation of Racah Coefficients 85
3.5.5 The Biedenharn Elliott Identity 88
3.5.6 The Hexagon Relation 90
3.5.7 Clebsch Gordan Coefficients
as Limits of Racah Coefficients 90
3.6 Tensor Operators and the Wigner Eckart Theorem 92
3.6.1 Tensor Operators for Compact Lie Groups 92
Table of Contents XI
3.6.2 Tensor Operators and the Wigner Eckart Theorem
for Ug(su2) 93
3.7 Applications 94
3.7.1 The Uq(sl2) Rotator Model of Deformed Nuclei 94
3.7.2 Electromagnetic Transitions in the Uq(sl2) Model 95
3.8 Notes 96
4. The Quantum Group SLg(2) and Its Representations 97
4.1 The Hopf Algebra O{SLq{2)) 97
4.1.1 The Bialgebra O(M,(2)) 97
4.1.2 The Hopf Algebra O(SLq(2)) 99
4.1.3 A Geometric Approach to SLq(2) 101
4.1.4 Real Forms of O{SLq{2)) 102
4.1.5 The Diamond Lemma 103
4.2 Representations of the Quantum Group SLq(2) 104
4.2.1 Finite Dimensional Corepresentations of O(SLq(2)):
Main Results 104
4.2.2 A Decomposition of O{SLq(2)) 105
4.2.3 Finite Dimensional Subcomodules of O(SLq(2)) 106
4.2.4 Calculation of the Matrix Coefficients 108
4.2.5 The Peter Weyl Decomposition of O(SLq{2)) 110
4.2.6 The Haar Functional of O(SLq(2)) Ill
4.3 The Compact Quantum Group SUq{2)
and Its Representations 113
4.3.1 Unitary Representations
of the Quantum Group SUq{2) 113
4.3.2 The Haar State
and the Peter Weyl Theorem for O(SUq(2)) 114
4.3.3 The Fourier Transform on 5(7,(2) 117
4.3.4 ^Representations and the C* Algebra of O{SUq{2)) .. 117
4.4 Duality of the Hopf Algebras Uq{s 2)
and O(SLq(2)) 119
4.4.1 Dual Pairing of the Hopf Algebras Uq(s 2)
and O(SLq(2)) 119
4.4.2 Corepresentations of O(SLq(2))
and Representations of Uq(sh) 123
4.5 Quantum 2 Spheres 124
4.5.1 A Family of Quantum Spaces for 51,(2) 124
4.5.2 Decomposition of the Algebra O(S^p) 126
4.5.3 Spherical Functions on S%p 129
4.5.4 An Infinitesimal Characterization of O(S*p) 129
4.6 Notes 132
XII Table of Contents
5. The g Oscillator Algebras and Their Representations 133
5.1 The Q Oscillator Algebras Acq and Aq 133
5.1.1 Definitions and Algebraic Properties 133
5.1.2 Other Forms of the g Oscillator Algebra 136
5.1.3 The g Oscillator Algebra
and the Quantum Algebra Uq{sl2) 137
5.1.4 The g Oscillator Algebras
and the Quantum Space Mq2 (2) 140
5.2 Representations of g Oscillator Algebras 140
5.2.1 iV Finite Representations 140
5.2.2 Irreducible Representations
with Highest (Lowest) Weights 141
5.2.3 Representations Without Highest and Lowest Weights 143
5.2.4 Irreducible Representations of Aq
for q a Root of Unity 145
5.2.5 Irreducible ^Representations of Aq and Aq 147
5.2.6 Irreducible ^Representations
of Another g Oscillator Algebra 148
5.3 The Fock Representation of the g Oscillator Algebra 149
5.3.1 The Fock Representation 149
5.3.2 The Bargmann Fock Realization 150
5.3.3 Coherent States 152
5.3.4 Bargmann Fock Space Realization
of Irreducible Representations of Uq(s 2) 153
5.4 Notes 154
Part II. Quantized Universal Enveloping Algebras
6. Drinfeld Jimbo Algebras 157
6.1 Definitions of Drinfeld Jimbo Algebras 157
6.1.1 Semisimple Lie Algebras 157
6.1.2 The Drinfeld Jimbo Algebras Uq(g) 161
6.1.3 The fc Adic Drinfeld Jimbo Algebras Uh(g) 165
6.1.4 Some Algebra Automorphisms
of Drinfeld Jimbo Algebras 167
6.1.5 Triangular Decomposition of Uq(g) 168
6.1.6 Hopf Algebra Automorphisms of Uq(g) 171
6.1.7 Real Forms of Drinfeld Jimbo Algebras 172
6.2 Poincare Birkhoff Witt Theorem and Verma Modules 173
6.2.1 Braid Groups 173
6.2.2 Action of Braid Groups on Drinfeld Jimbo Algebras .. 174
6.2.3 Root Vectors and Poincare Birkhoff Witt Theorem ... 175
6.2.4 Representations with Highest Weights 177
6.2.5 Verma Modules 179
Table of Contents XIII
6.2.6 Irreducible Representations with Highest Weights .... 180
6.2.7 The Left Adjoint Action of Uq(g) 181
6.3 The Quantum Killing Form and the Center of Uq(g) 184
6.3.1 A Dual Pairing of the Hopf Algebras Uq(b+)
and C/,(b_)op 184
6.3.2 The Quantum Killing Form on Uq(g) 187
6.3.3 A Quantum Casimir Element 189
6.3.4 The Center of Uq(g)
and the Harish Chandra Homomorphism 192
6.3.5 The Center of Uq(g) for q a Root of Unity 194
6.4 Notes 196
7. Finite Dimensional Representations
of Drinfeld—Jimbo Algebras 197
7.1 General Properties of Finite Dimensional Representations
oft/,(fl) 197
7.1.1 Weight Structure and Classification 197
7.1.2 Properties of Representations 200
7.1.3 Representations of /i Adic Drinfeld Jimbo Algebras .. . 202
7.1.4 Characters of Representations and Multiplicities
of Weights 203
7.1.5 Separation of Elements of Uq(g) 204
7.1.6 The Quantum Trace
of Finite Dimensional Representations 205
7.2 Tensor Products of Representations 207
7.2.1 Multiplicities in Tensor Products of Representations .. 208
7.2.2 Clebsch Gordan Coefficients 211
7.3 Representations of Uq(gln) for q not a Root of Unity 212
7.3.1 The Hopf Algebra Uq(g n) 212
7.3.2 Finite Dimensional Representations of Uq(gln) 213
7.3.3 Gel fand Tsetlin Bases and Explicit Formulas
for Representations 214
7.3.4 Representations of Class 1 217
7.3.5 Tensor Products of Representations 218
7.3.6 Tensor Operators and the Wigner Eckart Theorem ... 219
7.3.7 Clebsch Gordan Coefficients
for the Tensor Product Tm®Tx 220
7.3.8 Clebsch Gordan Coefficients
for the Tensor Product Tm ® Tp 221
7.3.9 The Tensor Product Tm ® 7 for q*1 0 224
7.4 Crystal Bases 225
7.4.1 Crystal Bases of Finite Dimensional Modules 226
7.4.2 Existence and Uniqueness of Crystal Bases 227
7.4.3 Crystal Bases of Tensor Product Modules 228
XIV Table of Contents
7.4.4 Globalization of Crystal Bases 229
7.4.5 Crystal Bases of C/£(n_) 230
7.5 Representations of Uq(g) for q a Root of Unity 232
7.5.1 General Results 232
7.5.2 Cyclic Representations 234
7.5.3 Cyclic Representations of the Algebra t/e(sl/+i) 235
7.5.4 Representations of Minimal Dimensions 237
7.5.5 Representations of Ue(sli+i) in Gel fand Tsetlin Bases 238
7.6 Applications 240
7.7 Notes 242
8. Quasitriangularity and Universal it Matrices 243
8.1 Quasitriangular Hopf Algebras 243
8.1.1 Definition and Basic Properties 243
8.1.2 .R Matrices for Representations 246
8.1.3 Square and Inverse of the Antipode 247
8.2 The Quantum Double and Universal .R Matrices 250
8.2.1 The Quantum Double of Skew Paired Bialgebras 250
8.2.2 Quasitriangularity of Quantum Doubles
of Finite Dimensional Hopf Algebras 254
8.2.3 The Rosso Form of the Quantum Double 257
8.2.4 Drinfeld Jimbo Algebras as Quotients
of Quantum Doubles 258
8.3 Explicit Form of Universal .R Matrices 259
8.3.1 The Universal .R Matrix for Uh(s 2) 259
8.3.2 The Universal .R Matrix for Uh(g) 261
8.3.3 .R Matrices for Representations of Ug(g) 264
8.4 Vector Representations and .R Matrices 267
8.4.1 Vector Representations of Drinfeld Jimbo Algebras ... 267
8.4.2 .R Matrices for Vector Representations 269
8.4.3 Spectral Decompositions of .R Matrices
for Vector Representations 272
8.5 // Operators and L Functionals 275
8.5.1 L Operators and .L Functionals 275
8.5.2 L Functionals for Vector Representations 277
8.5.3 The Extended Hopf Algebras f/?ext(0) 281
8.5.4 L Functionals for Vector Representations of Uq(g) .... 283
8.5.5 The Hopf Algebras U(R) and U£(b) 285
8.6 An Analog of the Brauer Schur Weyl Duality 288
8.6.1 The Algebras Uq(soN) 288
8.6.2 Tensor Products of Vector Representations 289
8.6.3 The Brauer Schur Weyl Duality
for Drinfeld Jimbo Algebras 291
8.6.4 Hecke and Birman Wenzl Murakami Algebras 293
8.7 Applications 294
Table of Contents XV
8.7.1 Baxterization 295
8.7.2 Elliptic Solutions
of the Quantum Yang Baxter Equation 297
8.7.3 ^ Matrices and Integrable Systems 298
8.8 Notes 300
Part III. Quantized Algebras of Functions
9. Coordinate Algebras of Quantum Groups
and Quantum Vector Spaces 303
9.1 The Approach of Faddeev Reshetikhin Takhtajan 303
9.1.1 The FRT Bialgebra A(R) 303
9.1.2 The Quantum Vector Spaces XL(f; R) and XR(f; R) . . 307
9.2 The Quantum Groups GLq(N) and SLq(N) 309
9.2.1 The Quantum Matrix Space Mq(N)
and the Quantum Vector Space C^ 310
9.2.2 Quantum Determinants 311
9.2.3 The Quantum Groups GLq(N) and SLq(N) 313
9.2.4 Real Forms of GLq(N) and SLq(N)
and * Quantum Spaces 316
9.3 The Quantum Groups Oq(N) and Spq(N) 317
9.3.1 The Hopf Algebras O(Oq(N)) and O(Spq(N)) 318
9.3.2 The Quantum Vector Space
for the Quantum Group Oq(N) 320
9.3.3 The Quantum Group SOq(N) 323
9.3.4 The Quantum Vector Space
for the Quantum Group Spq(N) 324
9.3.5 Real Forms of Oq(N) and Spq(N)
and * Quantum Spaces 325
9.4 Dual Pairings of Drinfeld Jimbo Algebras
and Coordinate Hopf Algebras 327
9.5 Notes 330
10. Coquasitriangularity and Crossed Product Constructions . 331
10.1 Coquasitriangular Hopf Algebras 331
10.1.1 Definition and Basic Properties 331
10.1.2 Coquasitriangularity of FRT Bialgebras A(R)
and Coordinate Hopf Algebras O{Gq) 337
10.1.3 L Functionals of Coquasitriangular Hopf Algebras .... 342
10.2 Crossed Product Constructions of Hopf Algebras 349
10.2.1 Crossed Product Algebras 349
10.2.2 Crossed Coproduct Coalgebras 352
10.2.3 Twisting of Algebra Structures by 2 Cocycles
and Quantum Doubles 354
XVI Table of Contents
10.2.4 Twisting of Coalgebra Structures by 2 Cocycles
and Quantum Codoubles 357
10.2.5 Double Crossed Product Bialgebras
and Quantum Doubles 359
10.2.6 Double Crossed Coproduct Bialgebras
and Quantum Codoubles 362
10.2.7 Realifications of Quantum Groups 363
10.3 Braided Hopf Algebras 365
10.3.1 Covariantized Products
for Coquasitriangular Bialgebras 365
10.3.2 Braided Hopf Algebras
Associated with Coquasitriangular Hopf Algebras .... 370
10.3.3 Braided Hopf Algebras
Associated with Quasitriangular Hopf Algebras 376
10.3.4 Braided Tensor Categories and Braided Hopf Algebras 377
10.3.5 Braided Vector Algebras 380
10.3.6 Bosonization of Braided Hopf Algebras 382
10.3.7 * Structures on Bosonized Hopf Algebras 386
10.3.8 Inhomogeneous Quantum Groups 388
10.3.9 * Structures for Inhomogeneous Quantum Groups .... 390
10.4 Notes 394
11. Corepresentation Theory and Compact Quantum Groups. 395
11.1 Corepresentations of Hopf Algebras 395
11.1.1 Corepresentations 395
11.1.2 Intertwiners 397
11.1.3 Constructions of New Corepresentations 397
11.1.4 Irreducible Corepresentations 398
11.1.5 Unitary Corepresentations 401
11.2 Cosemisimple Hopf Algebras 402
11.2.1 Definition and Characterizations 402
11.2.2 The Haar Functional of a Cosemisimple Hopf Algebra. 404
11.2.3 Peter Weyl Decomposition
of Coordinate Hopf Algebras 408
11.3 Compact Quantum Group Algebras 415
11.3.1 Definitions and Characterizations of CQG Algebras ... 415
11.3.2 The Haar State of a CQG Algebra 419
11.3.3 C* Algebra Completions of CQG Algebras 420
11.3.4 Modular Properties of the Haar State 422
11.3.5 Polar Decomposition of the Antipode 426
11.3.6 Multiplicative Unitaries of CQG Algebras 427
11.4 Compact Quantum Group C* Algebras 429
11.4.1 CQG C* Algebras and Their CQG Algebras 429
11.4.2 Existence of the Haar State of a CQG C Algebra 431
11.4.3 Proof of Theorem 39 433
Table of Contents XVII
11.4.4 Another Definition of CQG C* Algebras 434
11.5 Finite Dimensional Representations of GLq(N) 435
11.5.1 Some Quantum Subgroups of GLq(N) 435
11.5.2 Submodules of Relative Invariant Elements 436
11.5.3 Irreducible Representations of GLq(N) 437
11.5.4 Peter Weyl Decomposition of O(GLq(N)) 439
11.5.5 Representations of the Quantum Group Uq(N) 441
11.6 Quantum Homogeneous Spaces 442
11.6.1 Definition of a Quantum Homogeneous Space 442
11.6.2 Quantum Homogeneous Spaces
Associated with Quantum Subgroups 443
11.6.3 Quantum Gel fand Pairs 445
11.6.4 The Quantum Homogeneous Space Uq(N l) Uq{N).. 447
11.6.5 Quantum Homogeneous Spaces
of Infinitesimally Invariant Elements 451
11.6.6 Quantum Projective Spaces 452
11.7 Notes 454
Part IV. Noncommutative Differential Calculus
12. Covariant Differential Calculus on Quantum Spaces 457
12.1 Covariant First Order Differential Calculus 457
12.1.1 First Order Differential Calculi on Algebras 457
12.1.2 Covariant First Order Calculi on Quantum Spaces .... 459
12.2 Covariant Higher Order Differential Calculus 461
12.2.1 Differential Calculi on Algebras 461
12.2.2 The Differential Envelope of an Algebra 462
12.2.3 Covariant Differential Calculi on Quantum Spaces .... 463
12.3 Construction of Covariant Differential Calculi
on Quantum Spaces 464
12.3.1 General Method 464
12.3.2 Covariant Differential Calculi
on Quantum Vector Spaces 467
12.3.3 Covariant Differential Calculus on C^
and the Quantum Weyl Algebra 468
12.3.4 Covariant Differential Calculi
on the Quantum Hyperboloid 471
12.4 Notes 472
13. Hopf Bimodules and Exterior Algebras 473
13.1 Covariant Bimodules 473
13.1.1 Left Covariant Bimodules 473
13.1.2 Right Covariant Bimodules 477
13.1.3 Bicovariant Bimodules (Hopf Bimodules) 477
XVIII Table of Contents
13.1.4 Woronowicz Braiding of Bicovariant Bimodules 480
13.1.5 Bicovariant Bimodules and Representations
of the Quantum Double 483
13.2 Tensor Algebras and Exterior Algebras
of Bicovariant Bimodules 485
13.2.1 The Tensor Algebra of a Bicovariant Bimodule 485
13.2.2 The Exterior Algebra of a Bicovariant Bimodule 488
13.3 Notes 490
14. Covariant Differential Calculus on Quantum Groups 491
14.1 Left Covariant First Order Differential Calculi 491
14.1.1 Left Covariant First Order Calculi
and Their Right Ideals 491
14.1.2 The Quantum Tangent Space 494
14.1.3 An Example: The 3D Calculus on SLq{2) 496
14.1.4 Another Left Covariant Differential Calculus
on SLq{2) 498
14.2 Bicovariant First Order Differential Calculi 498
14.2.1 Right Covariant First Order Differential Calculi 498
14.2.2 Bicovariant First Order Differential Calculi 499
14.2.3 Quantum Lie Algebras
of Bicovariant First Order Calculi 500
14.2.4 The 4D+ and the 4D_ Calculus on SLq(2) 504
14.2.5 Examples of Bicovariant First Order Calculi
on Simple Lie Groups 505
14.3 Higher Order Left Covariant Differential Calculi 506
14.3.1 The Maurer Cartan Formula 506
14.3.2 The Differential Envelope of a Hopf Algebra 507
14.3.3 The Universal DC of a Left Covariant FODC 508
14.4 Higher Order Bicovariant Differential Calculi 511
14.4.1 Bicovariant Differential Calculi
and Differential Hopf Algebras 511
14.4.2 Quantum Lie Derivatives and Contraction Operators. . 514
14.5 Bicovariant Differential Calculi
on Coquasitriangular Hopf Algebras 517
14.6 Bicovariant Differential Calculi
on Quantized Simple Lie Groups 521
14.6.1 A Family of Bicovariant First Order
Differential Calculi 521
14.6.2 Braiding and Structure Constants of the FODC r±,z . 524
14.6.3 A Canonical Basis for the Left Invariant 1 Forms 525
14.6.4 Classification of Bicovariant First Order
Differential Calculi 527
14.7 Notes 528
Table of Contents XIX
Bibliography 529
Index 545
|
| any_adam_object | 1 |
| author | Klimyk, Anatolij U. 1939-2008 Schmüdgen, Konrad 1947- |
| author_GND | (DE-588)115774580 (DE-588)115774599 |
| author_facet | Klimyk, Anatolij U. 1939-2008 Schmüdgen, Konrad 1947- |
| author_role | aut aut |
| author_sort | Klimyk, Anatolij U. 1939-2008 |
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| callnumber-search | QC20.7.G76 |
| callnumber-sort | QC 220.7 G76 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 260 SK 340 UK 3000 |
| classification_tum | MAT 208f PHY 012f |
| ctrlnum | (OCoLC)37928561 (DE-599)BVBBV011626653 |
| dewey-full | 530.15/51255 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15/51255 |
| dewey-search | 530.15/51255 |
| dewey-sort | 3530.15 551255 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV011626653 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:15:52Z |
| institution | BVB |
| isbn | 3540634525 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007834260 |
| oclc_num | 37928561 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-703 DE-824 DE-91G DE-BY-TUM DE-384 DE-1050 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-19 DE-BY-UBM DE-703 DE-824 DE-91G DE-BY-TUM DE-384 DE-1050 DE-634 DE-83 DE-11 DE-188 |
| physical | XIX, 552 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts and monographs in physics |
| spellingShingle | Klimyk, Anatolij U. 1939-2008 Schmüdgen, Konrad 1947- Quantum groups and their representations Groupes quantiques Groupes quantiques ram Représentations de groupe ram Représentations de groupes Quantum groups Representations of quantum groups Quantengruppe (DE-588)4252437-4 gnd |
| subject_GND | (DE-588)4252437-4 |
| title | Quantum groups and their representations |
| title_auth | Quantum groups and their representations |
| title_exact_search | Quantum groups and their representations |
| title_full | Quantum groups and their representations Anatoli Klimyk ; Konrad Schmüdgen |
| title_fullStr | Quantum groups and their representations Anatoli Klimyk ; Konrad Schmüdgen |
| title_full_unstemmed | Quantum groups and their representations Anatoli Klimyk ; Konrad Schmüdgen |
| title_short | Quantum groups and their representations |
| title_sort | quantum groups and their representations |
| topic | Groupes quantiques Groupes quantiques ram Représentations de groupe ram Représentations de groupes Quantum groups Representations of quantum groups Quantengruppe (DE-588)4252437-4 gnd |
| topic_facet | Groupes quantiques Représentations de groupe Représentations de groupes Quantum groups Representations of quantum groups Quantengruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007834260&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT klimykanatoliju quantumgroupsandtheirrepresentations AT schmudgenkonrad quantumgroupsandtheirrepresentations |
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Branch Library Mathematics & Informatics
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0102 PHY 012f 2001 A 20777
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| Copy 1 | Available for loan On Shelf |
Branch Library Physics
| Call Number: |
0202 PHY 012f 2002 A 2546
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