量子群

出版时间：2000-6  出版社：北京世图  作者：Christian Kassel  页数：531  
Tag标签：无  

内容概要

量子群，ISBN：9787506247153，作者：法Christian Kassel著

书籍目录

PrefacePart 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 2Part 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-BialgebrasPart 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 InvariantReferencesIndex

用户评论 (总计2条)

•   这本书是一本专业书籍，很有实用价值。很好
•   印刷质量真的很差，为什么纸就不能放好一点的呢？Springer出版社的这套GTM教材确实很不错，就这印刷真是坑爹！