A quantum groups primer

書誌事項

A quantum groups primer

Shahn Majid

(London Mathematical Society lecture note series, 292)

Cambridge University Press, 2002

  • : pbk

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注記

Bibliography: p. 166

Includes index

内容説明・目次

内容説明

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.

目次

  • 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.

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詳細情報

  • NII書誌ID(NCID)
    BA56502073
  • ISBN
    • 0521010411
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge ; New York
  • ページ数/冊数
    x, 169 p.
  • 大きさ
    23 cm
  • 件名
  • 親書誌ID
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