量子群(英文版)

量子群(英文版)

作者:., 出版社:世界圖書出版公司, 出版日期:2000-06-01

商品條碼:9787506247153, ISBN:7506247151
分類標籤:數學 » 物理 » 自然科普與應用科學

 

內容簡介

量子群(英文版)

【目錄】
Preface
Part One Quantum SL 2
  Ⅰ  Preliminaries
    1 Algebras and Modules
    2 Free Algebras
    3 The Affine Line and Plane
    4 Matrix Multiplication
    5 Determinants and Invertible Matrices
    6 Graded and Filtered Algebras
    7 Ore Extensions
    8 Noetherian Rings
    9 Exercises
    10 Notes
  Ⅱ  Tensor Products
    1 Tensor Products of Vector Spaces
    2 Tensor Products of Linear Maps
    3 Duality and Traces
    4 Tensor Products of Algebras
    5 Tensor and Symmetric Algebras
    6 Exercises
    7 Notes
  Ⅲ  The Language of Hopf Algebras
    1 Coalgebras
    2 Bialgebras
    3 Hopf Algebras
    4 Relationship with Chapter I. The Hopf Algebras GL 2and SL 2
    5 Modules over a Hopf Algebra
    6 Comodules
    7 Comodule-Algebras. Coaction of SL 2 on the Affine Plane
    8 Exercises
    9 Notes
  Ⅳ  The Quantum Plane and Its Symmetries
    1 The Quantum Plane
    2 Gauss Polynomials and the q-Binomial Formula
    3 The Algebra Mq 2
    4 Ring-Theoretical Properties of Mq 2
    5 Bialgebra Structure on Mq 2
    6 The Hopf Algebras GLq 2 and SLq 2
    7 Coaction on the Quantum Plane
    8 Hopf *-Algebras
    9 Exercises
    10 Notes
  Ⅴ  The Lie Algebra of SL 2
    1 Lie Algebras
    2 Enveloping Algebras
    3 The Lie Algebra sl 2
    4 Representations of sl 2
    5 The Clebsch-Gordan Formula
    6 Module-Algebra over a Bialgebra. Action of sl 2 on the Affine Plane
    7 Duality between the Hopf Algebras U sl 2 and SL 2
    8 Exercises
    9 Notes
  Ⅵ  The Quantum Enveloping Algebra of 5[ 2
    1 The Algebra Uq sl 2
    2 Relationship with the Enveloping Algebra of 5[ 2
    3 Representations of Uq
    4 The Harish-Chandra Homomorphism and the Centre of Uq
  Ⅶ  A Hopf Algebra Structure on Uq Sl 2
Part Two  Universal R-Matrices
  Ⅷ  The Yang-Baxter Equation and Co Braided Bialgebras
  Ⅸ  Drinfeld''s Quantum Double
Part Three Low-Dimensional Topology and Tensor Categories
  Ⅹ  Knots, Links, Tangles, and Braids
  Ⅺ  Tensor Categories
  Ⅻ  The Tangle Category
  ⅩⅢ  Braidings
  ⅩⅣ  Duality in Tensor Categories
  ⅩⅤ  Quasi-Bialgebras
Part Four Quantum Groups and Monodromy
  ⅩⅥ  Generalities on Quantum Enveloping Algebras
  ⅩⅦ  Drinfeld and Jimbo''s Quantum Enveloping Algebras
  ⅩⅧ  Cohomology and Rigidity Theorems
  ⅩⅨ  Monodromy of the Knizhnik-Zamolodchikov Equations
  ⅩⅩ  Postlude. A Universal Knot Invariant
References
Index

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