基本信息

书名:量子群入门

定价：75.00元

作者:(美)沙里　著

出版社：世界图书出版公司

出版日期：2010_04_01

ISBN：9787510005770

字数：

页码：654

版次：1

装帧：平装

开本：24开

商品重量：

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内容提要

quantum groups first arose in the physics literature, particularly in the work of L. D. Faddeev and the Leningrad school, from the 'inverse scattering method', which had been developed to construct and solve 'integrable' quantum systems. They have excited great interest in the past few years because of their unexpected connections with such, at first sight, unrelated parts of mathematics as the construction of knot invariants and the representation theory of algebraic groups in characteristic p.
　　In their original form, quantum groups are associative algebras whose defin_ing relations are expressed in terms of a matrix of constants (depending on the integrable system under consideration) called a quantum R_matrix. It was realized independently by V. G. Drinfel'd and M. Jimbo around 1985 that these algebras are Hopf algebras, which, in many cases, are deformations of 'universal enveloping algebras' of Lie algebras. A little later, Yu. I. Manin and S. L. Woronowicz independently constructed non_commutative deforma_tions of the algebra of functions on the groups SL2(C) and SU2, respectively,and showed that many of the classical results about algebraic and topological groups admit analogues in the non_commutative case.

目录

Introduction
1 Poisson_Lie groups and Lie bialgebras
　1.1 Poisson manifolds
　1.2 Poisson_Lie groups
　1.3 Lie bialgebras
　1.4 Duals and doubles
　1.5 Dressing actions and symplectic leaves
　1.6 Deformation of Poisson structures and quantization
　Bibliographical notes
2 Coboundary Poisson_Lie groups and the classical Yang_Baxter equation
　2.1 Coboundary Lie bialgebras
　2.2 Coboundary Poisson_Lie groups
　2.3 Classical integrable systems
　Bibliographical notes
3 Solutions of the classical Yang_Baxter equation
　3.1 Constant solutions of the CYBE
　3.2 Solutions of the CYBE with spectral parameters
　Bibliographical notes
4 Quasitriangular Hopf algebras
　4.1 Hopf algebras
　4.2 Quasitriangular Hopf algebras
　Bibliographical notes
5 Representations and quasitensor categories
　5.1 Monoidal categories
　5.2 Quasitensor categories
　5.3 Invariants of ribbon tangles
　Bibliographical notes
6 Quantization of Lie bialgebras
　6.1 Deformations of Hopf algebras
　6.2 Quantization
　6.3 Quantized universal enveloping algebras
　6.4 The basic example
　6.5 Quantum Kac_Moody algebras
　Bibliographical notes
7 Quantized function algebras
　7.1 The basic example
　7.2 R_matrix quantization
　7.3 Examples of quantized function algebras
　7.4 Differential calculus on quantum groups
　7.5 Integrable lattice models
　Bibliographical notes
8 Structure of QUE algebras:the universal R_matrix
　8.1 The braid group action
　8.2 The quantum Weyl group
　8.3 The quasitriangular structure
　Bibliographical notes
9 Specializations of QUE algebras
　9.1 Rational forms
　9.2 The non_restricted specialization
　9.3 The restricted specialization
　9.4 Automorphisms and real forms
　Bibliographical notes
10 Representations of QUE algebras: 　the generic casa
　10.1 Classification of finite_dimensional representations
　10.2 Quantum invariant theory
　Bibliographical notes
11 Representations of QUE algebras:the root of unity case
　11.1 The non_restricted case
　11.2 The restricted case
　11.3 Tilting modules and the fusion tensor product
　Bibliographical notes
12 Infinite_dimensional quantum groups
　12.1 Yangians and their representations
　12.2 Quantum afiine algebras
　12.3 Frobenius_Schur duality for Yangians and quantum affine algebras
　12.4 Yangians and infinite_dimensional classical groups
　12.5 Rational and trigonometric solutions of the QYBE
　Bibliographical notes
13 Quantum harmonic analysis
　13.1 Compact quantum groups and their representations
　13.2 Quantum homogeneous spaces
　13.3 Compact matrix quantum groups
　13.4 A non_compact quantum group
　13.5 q_special functions
　Bibliographical notes
14 Canonical bases
　14.1 Crystal bases
　14.2 Lusztig's canonical bases
　Bibliographical notes
15 Quantum group invariants of knots and 3_manifolds
　15.1 Knots and 3_manifolds: a quick review
　15.2 Link invariants from quantum groups
　15.3 Modular Hopf algebras and 3_manifold invariants
　Bibliographical notes
16 Quasi_Hopf algebras and the Knizhnik_Zamolodchikov equation
　16.1 Quasi_Hopf algebras
　16.2 The Kohno_Drinfel'd monodromy theorem
　16.3 Affine Lie algebras and quantum groups
　16.4 Quasi_Hopf algebras and Grothendieck's esquisse
　Bibliographical notes
Appendix Kac_Moody algebras
　A 1 Generalized Cartan matrices
　A 2 Kac_Moody algebras
　A 3 The invariant bilinear form
　A 4 Roots
　A 5 The Weyl group
　A 6 Root vectors
　A 7 Aide Lie algebras
　A 8 Highest weight modules
References
Index of notation
General index

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