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Frohlich J. — Quantum Groups, Quantum Categories And Quantum Field Theory
Frohlich J. — Quantum Groups, Quantum Categories And Quantum Field Theory

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Название: Quantum Groups, Quantum Categories And Quantum Field Theory

Автор: Frohlich J.

Аннотация:

This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 440

Добавлена в каталог: 25.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A_{n}$ categories, braided      385
$A_{n}$ categories, monoidal      372
*-endomorphism      23
A-type categories      390 396 407
Abelian categories      177
Adjoint representation      103
Antipode      103
Anyons      20
Automorphisms (invertible objects)      61
Balanced categories      181 222
Bihomomorphic forms      211
Borel algebra      105
Braid goup representations      41 141 142
Braid goup statistics      21
Braided (tensor) categories      179
C*-quantum categories      181
Cabeling      383
Canonical generator      85
Cartan involution      114
Casimir      130
Causally independent      32
Center variety      124
Charge-transport operator      28
Charged fields      31
Chebychev polynomials      75
Classification categories      409
Classification, fusionrules      97
Coassociativity      103
Cohomology of groups      254
Comultiplication      102
Conjugate reps (of Quantumgroups)      121
Conjugation (of Quantumgroup)      114
Covariance      25
DGA-algebra      249
Dimensions, Perron Frobenius      56
Dimensions, q-      137 361
Dimensions, statistical      39
Direct sums      177
Double complex      250
Double construction      112
Duality      28 84 184
Eilenberg MacLane spaces      250
Field algebra      192
Finite categories      177
Frobenius imprimitivity index      52
Fusion rule algebra      46
Fusion rule algebra homomorphisms, coherent      293
Fusion rule algebra homomorphisms, graded      294
Fusion rule algebra homomorphisms, irreducible      289
Fusion rule algebra scalarproduct      46
Fusion rule algebra subalgebra      47
Fusion rule algebra, conjugation in      46
Fusion rule algebra, crossed product of      66
Fusion rule algebra, rational      177
Fusion rule algebra, representation of      48
Fusion rule algebra, star product of      63
Fusion rule algebra, support in      54
Fusion rule algebra, twisted      63
Fusion rule matrix      39 48
Grading      62
Grading, universal      63
Group extension, abelian      256 267
Group extension, central      267
Haag duality      27
Hexagonal equation, modified (projective)      344 379
Highest weight reps      120
Highest weight reps, invariant forms of      120
Homology of groups      245
Hopf algebra      102
Hopf algebra, quasi-      103
Hopf algebra, quasitriangular      102
Iinvertible objects      60
Incidence matrix      68 72
Index(subfactors)      40 186 197
Induced categories      288 295 316 322
Kunneth formula      248
Local commutation relations      193
Locality      22 25
Markov trace      43 171 174 189
Modular extension      187
monodromy      162 229 323
Observable algebra      22
Operator product expansion      195
Path algebra      143
Path space      142
Path space, restricted      147
Pentagonal equation      178
Pentagonal equation structure constants      179
Pentagonal equation, modified (projective)      344
Permutation group statistics      41
Perron Frobenius algebra      56
Perron Frobenius dimension      54
Perron Frobenius eigenvector      52
Polyhedral groups      89
Polynomial equations      38
Product categories      285
Pseudoreal objects      186 271
Pullback categories      297
q-dimension      137 361
q-numbers      118
Quadratic (Whitehead) group      252
Quantum categories      180
Rational fusion rules      177
Rational quantum theory      45
Real objects      186 242 271
Reduced categories      177
Representation categories      182
Rigid categories      180
Signature-extendable subgroups      347
Simple domain      25
Space-like cone      25 27
Spin      33 222
Spin, standard $A_{n}$      239
Stabilizer of objects      202
Star involution (of Quantumgroups)      114
Statistical dimension      39
Statistical phase      222
Statistics parameter      43 171
Strict categories      179
Subobjects      177
Superselection sector      27
Suspension      251 260
Symmetric categories      179
Temperley — Lieb algebra      188 219
Tensor (monoidal) categories      178
Tensor product of categories      178
Tensor product, Quantumgroup reps      121 126
Theta categories      245
Theta categories, group of      271
Theta categories, group of, graded action      287
Theta categories, Hopf algebra for      280
Theta categories, structure matrices of      266 277
Unitary representations of Quantumgroups      121 125 169
Universal coefficient theorem      254
Vacuum representation      26
Vertex sos transformation      141
Yang — Baxter equation      33 104 206
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