量子群入門

《量子群入門》是2010年世界圖書出版公司出版圖書，作者是沙里。

基本介紹

• 中文名：量子群入門
• 作者：沙里(Chari.V.)
• 出版社：世界圖書出版公司
• 出版時間：2010年4月1日
• 定價：75 元
• 開本：16 開
• ISBN：9787510005770

內容簡介

This reprint edition for the People's Republic of China is published by arrange-ment with the Press Syndicate ofthe University ofCambridge，Cambridge，Unit-ed Kingdom.@ mbridge University Press&Beijing Wodd Publishing Corporation 2010This book is in copyrighL No reproduction of any part may take place without thewritten permission of Cambridge University Press or Bering Wodd Publishing orporation his edition is for sale in the mainland of China only，excluding Hong KongSAR，Macao SAR and Taiwan，and may not be bought for export here.

A Guide to Quantum Groups，1 st ed.（978-0-521-55884-6）by Vyjayanthi haff&Andrew Pressley first published by Cambridge University Press 1994All rights reserved。

圖書目錄

Introduction

1 Poisson-Lie groups and Lie bialgebras

1.1 Poisson manifolds

A Definitions

B Functorial properties

C Symplectic leaves

1.2 Poisson-Lie groups

A Definitions

B Poisson homogeneous spaces

1.3 Lie bialgebras

A The Lie bialgebra of a Poisson-Lie group

B Martintriples

C Examples

D Derivations

1.4 Duals and doubles

A Duals of Lie bialgebras and Poisson-Lie groups

B The classical double

C Compact Poisson-Lie groups

1.5 Dressing actions and symplectic leaves

A Poisson actions

B Dressing transformations and symplectic leaves

C Symplectic leaves in compact Poisson-Lie groups

D Thetwsted ease

1.6 Deformation of Poisson structures and quantization

A Deformations of Poisson algebras

BWeylquantization

C Quantization as deformation

Bibliographical notes

2 Coboundary PoissoI-Lie groups and the classical Yang-Baxter equation

2.1 Coboundary Lie bialgebras

A Definitions

B The classical Yang-Baxter equation

C Examples

D The classical double

2.2 Coboundary Poisson-Lie groups

A The Sklyanin bracket

B r-matrices and 2-cocycles

CThe classicalR-matrix

2 3 Classical integrable systems

A Complete integrability

B Lax pairs

C Integrable systems from r-matrices

D Toda systems

Bibliographical notes

3 Solutions of the classical Yang-Baxterequation

3.1 Constant solutions of the CYBE

A The parameter space of non.skew solutions

B Description of the solutions

C Examples

D Skew solutions and quasi-Frobenins Lie algebras

3.2 Solutions of the CYBE with spectral parameters

A Clnssification ofthe solutions

B Elliptic solutions

C Trigonometrie solutions

D Rational solutions

B ibliographical notes

4 Quasitriangular Hopf algebras

4.1 Hopf algebras

A Definitions

B Examples

C Representations of Hopf algebras

D Topological Hopf algebras and duMity

E Integration Oll Hopf algebras

F Hopf-algebras

4.2 Quasitriangular Hopf algebras

A Almost cocommutative Hopf algebras

B Quasitriangular Hopf algebras

C Ribbon Hopf algebras and quantum dimension

D The quantum double

E Twisting

F Sweedler'8 example

Bibliographical notes

5 Representations and quasitensor categories

5.1 Monoidal categories

A Abelian categories

B Monoidal categories

C Rigidity

D Examples

E Reconstruction theorems

5.2 Quasitensor categories

ATensorcategories

B Quasitensor categories

C Balancing

D Quasitensor categories and fusion rules

EQuasitensorcategoriesin quantumfieldtheory

5.3 Invariants of ribbon tangles

A Isotopy invariants and monoidal functors

B Tangleinvariants

CCentral ek！ments

Bibliographical notes

6 Quantization of Lie bialgebras

6.1 Deformations of Hopf algebras

A Defmitions

B Cohomologytheory

CIugiditytheorems

6.2 Quantization

A（Co-）Poisson Hopfalgebras

B Quantization

C Existence of quantizations

6.3 Quantized universal enveloping algebras

ACocommut&tiveQUE algebras

B Quasitriangular QUE algebras

CQUE duals and doubles

D The square of the antipode

6.4 The basic example

A Constmctmn of the standard quantization

B Algebra structure

C PBW basis

D Quasitriangular structure

ERepresentations

F A non-standard quantization

6.5 Quantum Kac-Moody algebras

A The-andard quantization

B The centre

C Multiparameter quantizations Bibliographical notes

7 Quantized function algebras

7.1 The basic example

A Definition

B A basis of.fn（sL2（c））

C TheR-matrixformulation

D Duality

E Representations

7.2 R-matrix quantization

A From It-matrices to bialgebras

B From bialgebras to Hopf algebras：the quantum determinant

C solutions oftheQYBE

7.3 Examples of quantized function algebras

A The general definition

B The quantum speciallinear group

C The quantum orthogonal and symplectic groups

D Multiparameter quantized function algebras

7.4 Differential calculus on quantum groups

A The de Rham complex ofthe quantum plane

BThe deRham complex ofthe quantum m×m matrices

CThedeRhamcomplex ofthe quantum generallinear group

DInvariantforms on quantumGLm

7.5 Integrable lattice models

AVertexmodels

BTransfermatrices

……

9 Specializations of QUE algebras

10 Representations of QUE algebas the generic case

11Representations of QUE algebas the root of unity case

12 Infinite-dimensionalquantum groups

13 Quantum harmonic analysis

14 Canonical bases

15 Quantum gruop invariants f knots and 3-manifolds

16 Quasi-Hopf algebras and the Knizhnik -Zamolodchikov equation