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By Shahn Majid
Publisher: Cambridge University Press
Print Publication Year:2002
Online Publication Date:January 2010
Online ISBN:9780511549892
Paperback ISBN:9780521010412
Book DOI: http://dx.doi.org/10.1017/CBO9780511549892
Subjects: Algebra , Mathematical Physics
Here is 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, the book is suitable as a primary text for graduate courses in quantum groups or supplementary reading for modern courses in advanced algebra. The material assumes knowledge of basic and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The volume is a primer for mathematicians but it will also be useful for mathematical physicists.
Reviews:
pp. i-vi
pp. vii-viii
pp. ix-x
1 - Coalgebras, bialgebras and Hopf algebras. Uq(b+): Read PDF
pp. 1-8
2 - Dual pairing. SLq(2). Actions: Read PDF
pp. 9-16
3 - Coactions. Quantum plane A2q: Read PDF
pp. 17-22
4 - Automorphism quantum groups: Read PDF
pp. 23-28
5 - Quasitriangular structures: Read PDF
pp. 29-33
6 - Roots of unity. uq(sl2): Read PDF
pp. 34-38
pp. 39-43
8 - Quantum double. Dual-quasitriangular structures: Read PDF
pp. 44-51
9 - Braided categories: Read PDF
pp. 52-57
10 - (Co)module categories. Crossed modules: Read PDF
pp. 58-63
11 - q-Hecke algebras: Read PDF
pp. 64-69
12 - Rigid objects. Dual representations. Quantum dimension: Read PDF
pp. 70-76
13 - Knot invariants: Read PDF
pp. 77-83
14 - Hopf algebras in braided categories. Coaddition on A2q: Read PDF
pp. 84-90
15 - Braided differentiation: Read PDF
pp. 91-97
16 - Bosonisation. Inhomogeneous quantum groups: Read PDF
pp. 98-104
17 - Double bosonisation. Diagrammatic construction of uq(sl2): Read PDF
pp. 105-112
18 - The braided group uq(n+). Construction of uq(g): Read PDF
pp. 113-119
19 - q-Serre relations: Read PDF
pp. 120-125
20 - R-matrix methods: Read PDF
pp. 126-131
21 - Group, algebra, Hopf algebra factorisations. Bicrossproducts: Read PDF
pp. 132-138
22 - Lie bialgebras. Lie splittings. Iwasawa decomposition: Read PDF
pp. 139-145
23 - Poisson geometry. Noncommutative bundles. q-Sphere: Read PDF
pp. 146-152
24 - Connections. q-Monopole. Nonuniversal differentials: Read PDF
pp. 153-158
pp. 159-165
pp. 166-166
pp. 167-169