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A Quantum Groups Primer

A Quantum Groups Primer

$79.99 (C)

Part of London Mathematical Society Lecture Note Series

  • Date Published: May 2002
  • availability: Available
  • format: Paperback
  • isbn: 9780521010412

$ 79.99 (C)
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About the Authors
  • 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.

    • Concise and self-contained introduction for mathematicians
    • Written in a clear and accessible style
    • Includes problem sets to aid study
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    Reviews & endorsements

    '… 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 MATH

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    Product details

    • Date Published: May 2002
    • format: Paperback
    • isbn: 9780521010412
    • length: 180 pages
    • dimensions: 228 x 152 x 17 mm
    • weight: 0.265kg
    • contains: 23 b/w illus. 50 exercises
    • availability: Available
  • Table of Contents

    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.

  • Author

    Shahn Majid, Queen Mary University of London

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