A quantum groups primer / Shahn Majid.

Format:

Book

Author/Creator:

Majid, Shahn.

Series:

London Mathematical Society lecture note series ; 292.

London Mathematical Society lecture note series

Language:

English

Subjects (All):

Quantum groups.

Physical Description:

x, 169 pages : illustrations ; 23 cm.

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2002.

Summary:

Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.

Contents:

1 Coalgebras, bialgebras and Hopf algebras. U[subscript q](b+) 1

2 Dual pairing. SL[subscript q](2). Actions 9

3 Coactions. Quantum plane A[superscript 2 subscript q] 17

4 Automorphism quantum groups 23

5 Quasitriangular structures 29

6 Roots of unity. u[subscript q](sl[subscript 2]) 34

7 q-Binomials 39

8 Quantum double. Dual-quasitriangular structures 44

9 Braided categories 52

10 (Co)module categories. Crossed modules 58

11 q-Hecke algebras 64

12 Rigid objects. Dual representations. Quantum dimension 70

13 Knot invariants 77

14 Hopf algebras in braided categories. Coaddition on A[superscript 2 subscript q] 84

15 Braided differentiation 91

16 Bosonisation. Inhomogeneous quantum groups 98

17 Double bosonisation. Diagrammatic construction of u[subscript q](sl[subscript 2]) 105

18 The braided group U[subscript q](n+). Construction of U[subscript q](g) 113

19 q-Serre relations 120

20 R-matrix methods 126

21 Group, algebra, Hopf algebra factorisations. Bicrossproducts 132

22 Lie bialgebras. Lie splittings. Iwasawa decomposition 139

23 Poisson geometry. Noncommutative bundles. q-Sphere 146

24 Connections. q-Monopole. Nonuniversal differentials 153.

Notes:

Includes bibliographical references (page 166) and index.

ISBN:

0521010411

OCLC:

48383475