A Quantum Groups Primer

כריכה קדמית
Cambridge University Press, 4 באפר׳ 2002 - 169 עמודים
This book provides a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes for the Part III pure mathematics course at Cambridge University, it is suitable for use as a textbook for graduate courses in quantum groups or as supplement to modern courses in advanced algebra. The book assumes a background knowledge of basic algebra and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The book is aimed as a primer for mathematicians but will also be useful for mathematical physicists.
 

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תוכן

1 Coalgebras bialgebras and Hopf algebras Uqb+
1
2 Dual pairing SLq2 Actions
9
3 Coactions Quantum plane A²q
17
4 Automorphism quantum groups
23
5 Quasitriangular structures
29
6 Roots of unity Uq5l2
34
7 qBinomials
39
8 Quantum double Dualquasitriangular structures
44
15 Braided differentiation
91
16 Bosonisation Inhomogeneous quantum groups
98
17 Double bosonisation Diagrammatic construction of uqsl2
105
18 The braided group Uqn+ Construction of Uqg
113
19 qSerre relations
120
20 Rmatrix methods
126
21 Group algebra Hopf algebra factorisations Bicrossproducts
132
22 Lie bialgebras Lie splittings Iwasawa decomposition
139

9 Braided categories
52
10 Comodule categories Crossed modules
58
11 qHecke algebras
64
12 Rigid objects Dual representations Quantum dimension
70
13 Knot invariants
77
14 Hopf algebras in braided categories Coaddition on òq
84
23 Poisson geometry Noncommutative bundles qSphere
146
24 Connections qMonopole Nonuniversal differentials
153
Problems
159
Bibliography
166
Index
167
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