The term "quanturn groups" was popularized by Drinfeld in his address to the International Congress of Mathematicians in Berkeley(1986). It stands for certain special Hopf algebras which are nontrivial deformations of the enveloping Hopf algebras of semisimple Lie algebras or of the algebras of regular functions on the corresponding algebraic groups. As was soon observed, quantum groups have close connections with varied, a priori remote, areas of mathematics and physics.
本书为英文版。
量子群（英文版）
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The term "quanturn groups" was popularized by Drinfeld in his address to the International Congress of Mathematicians in Berkeley(1986). It stands for certain special Hopf algebras which are nontrivial deformations of the enveloping Hopf algebras of semisimple Lie algebras or of the algebras of regular functions on the corresponding algebraic groups. As was soon observed, quantum groups have close connections with varied, a priori remote, areas of mathematics and physics.
本书为英文版。 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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