《量子群入门》 内容简介:A Guide to Quantum Gro演耐ups，1 st ed.(978-0-521-55884-6)by Vyjayanthi haff&Andrew Pressley fi来自rst pub360百科lished by Cambridge University Press 1994All rights reserved

• 书名 量子群入门
• 作者 沙里(Chari.V.)
• ISBN 9787510005770
• 定价 75.00元
• 出版社 世界图书出版公司

内容简介

　　This repr来自int edition for the People's Republic of China is published by arrange-ment with the Press Syndicate ofthe Universit织女叶y ofCambridge，Cambridge，Unit-ed Kin360百科gdom.@ mbridge University Press&Beijing Wodd Publishing Corporation 2010This book 以血价坚装条置步号附任is in copyri修识下转威艺作ghL No reproduction of any part may take place without thewritten permiss硫抗态白关住取些模冲妈ion of Cambrid倍镇如清的济ge University Press or Bering Wodd Publishing orporation his edit报级模殖ion is for sale in the mainland of China only，excluding Hong K算ongSAR，Macao SAR and Taiwan，and may not be bought for export h计游打置附呢酒ere.

图书目录

　　Intro战体duction

　　1 Pois开除卷son-Lie groups and Lie bialgebras

　　1.1 Po类停获继杀isson manifolds

　　A Definitions

　　B Functorial 包粉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

　批距曾波者气由限蛋住卷　B Martintriples

　　C Examples

　　D Derivat吗探力帮千ions

　　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 Dressi革云王教至ng action效游化经原措八力格最s and symplectic leaves

　　A Poisson actions

　　B D委孔答飞盟张一罪儿加吃ressing transformations 紧执妈日感缩殖概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