A Quantum Groups Primer
Published on 4. April 2002
Book
Paperback/Softback
180 pages
978-0-521-01041-2 (ISBN)
Description
This book provides a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes from a Part III pure mathematics course at Cambridge University, it is suitable for use as a textbook for graduate courses in quantum groups or as a 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 and takes a modern approach leading into knot theory, braided categories and noncommutative differential geometry. It should also be useful for mathematical physicists.
Reviews / Votes
'... would serve admirably - as the author suggests - as the basis for a taught graduate course ... this book is a clearly written painless read. I can recommend this text as an entry work for those wishing to acquaint themselves with the still popular topic of quantum groups.' A. I. Solomon, Contemporary Physics 'Many intuitive comments and informal remarks, a well chosen set of main examples used systematically in the book and a clear and understandable style make the book very comfortable and useful for students as well as for mathematicians from other fields.' EMS Newsletter 'This monograph is an excellent reference (and often a true 'eye-opener') for researchers working in quantum groups ... S. Majid is well-known for his lively and very informative style of writing, and the reviewed book confirms this opinion. Thus the book is very well written, the proofs contain enough details to make them easily readable but still challenging enough to keep students interested ... I can full-heartily recommend this work as a basis for a one-term postgraduate course or as an introductory text to all mathematicians who would like to learn quickly the main ideas, techniques and wide range of applications of quantum group theory.' Zentralblatt MATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises; 23 Line drawings, unspecified
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 10 mm
Weight
270 gr
ISBN-13
978-0-521-01041-2 (9780521010412)
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Schweitzer Classification
Other editions
Additional editions
Shahn Majid
A Quantum Groups Primer
E-Book
03/2011
1st Edition
Cambridge University Press
€63.49
Available for download
Person
Content
Preface; 1. Coalgebras, bialgebras and Hopf algebras. Uq(b+); 2. Dual pairing. SLq(2). Actions; 3. Coactions. Quantum plane A2q; 4. Automorphism quantum groups; 5. Quasitriangular structures; 6. Roots of Unity. uq(sl2); 7. q-Binomials; 8. quantum double. Dual-quasitriangular structures; 9. Braided categories; 10 (Co)module categories. Crossed modules; 11. q-Hecke algebras; 12. Rigid objects. Dual representations. Quantum dimension; 13. Knot invariants; 14. Hopf algebras in braided categories; 15. Braided differentiation; 16. Bosonisation. Inhomogeneous quantum groups; 17. Double bosonisation. Diagrammatic construction of uq(sl2); 18. The braided group Uq(n-). Construction of Uq(g); 19. q-Serre relations; 20. R-matrix methods; 21. Group algebra, Hopf algebra factorisations. Bicrossproducts; 22. Lie bialgebras. Lie splittings. Iwasawa decomposition; 23. Poisson geometry. Noncommutative bundles. q-Sphere; 24. Connections. q-Monopole. Nonuniversal differentials; Problems; Bibliography; Index.