量子群（英文版）

量子群（英文版）

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作者: C.Kassel 著

出版社: 世界图书出版公司

出版时间: 2000-06

版次: 1

ISBN: 9787506247153

定价: 89.00

装帧: 平装

开本: 其他

纸张: 胶版纸

页数: 531页

分类: 自然科学

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
目录:
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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