Foundations of Quantum Group Theory

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Cambridge University Press, Apr 13, 2000 - Mathematics - 640 pages
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This is a graduate-level text that systematically develops the foundations of the subject. Quantum groups (i.e. Hopf algebras) are treated as mathematical objects in their own right; basic properties and theorems are proven in detail from this standpoint, including the results underlying key applications. After formal definitions and basic theory, the book goes on to cover such topics as quantum enveloping algebras, matrix quantum groups, combinatorics, cross products of various kinds, the quantum double, the semiclassical theory of Poisson-Lie groups, the representation theory, braided groups and applications to q-deformed physics. The explicit proofs and a great many worked examples and exercises will allow readers to quickly pick up the techniques needed for working in this exciting new field.
  

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Contents

I
vii
II
xi
III
1
IV
5
V
6
VI
12
VII
15
VIII
17
XLIII
225
XLIV
239
XLV
262
XLVI
286
XLVII
297
XLVIII
302
XLIX
304
L
314

IX
22
X
28
XI
36
XII
38
XIII
39
XIV
50
XV
55
XVI
65
XVII
70
XVIII
72
XIX
73
XX
85
XXI
95
XXII
102
XXIII
105
XXIV
108
XXV
111
XXVI
128
XXVII
143
XXVIII
149
XXIX
153
XXXI
163
XXXII
166
XXXIII
173
XXXIV
178
XXXV
180
XXXVI
191
XXXVII
192
XXXVIII
197
XXXIX
204
XL
209
XLI
220
XLII
223
LI
335
LII
344
LIII
360
LIV
364
LV
366
LVI
383
LVII
395
LVIII
420
LIX
432
LX
436
LXI
438
LXII
451
LXIII
465
LXIV
489
LXV
490
LXVI
499
LXVII
520
LXVIII
527
LXIX
530
LXX
540
LXXI
555
LXXII
568
LXXIII
588
LXXIV
589
LXXV
593
LXXVI
599
LXXVII
606
LXXVIII
611
LXXIX
625
LXXX
629
LXXXI
640
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About the author (2000)

Shahn Majid is Professor of Mathematics at Queen Mary, University of London. Trained as a theoretical physicist and mathematician at Cambridge and Harvard, he helped pioneer the theory of quantum symmetry in the 1980s and 1990s. He is author of two textbooks in the field and numerous research articles.

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