TOP
0
0
三民出版.新書搶先報|最速、最優惠的新鮮貨報給你知!
量子群入門(簡體書)
滿額折

量子群入門(簡體書)

商品資訊

人民幣定價:75 元
定價
:NT$ 450 元
優惠價
87392
絕版無法訂購
商品簡介
目次
相關商品

商品簡介

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. Drinfeld 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.

目次

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 Lusztigs 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-Drinfeld monodromy theorem
 16.3 Affine Lie algebras and quantum groups
 16.4 Quasi-Hopf algebras and Grothendiecks 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

您曾經瀏覽過的商品

購物須知

大陸出版品因裝訂品質及貨運條件與台灣出版品落差甚大,除封面破損、內頁脫落等較嚴重的狀態,其餘商品將正常出貨。

特別提醒:部分書籍附贈之內容(如音頻mp3或影片dvd等)已無實體光碟提供,需以QR CODE 連結至當地網站註冊“並通過驗證程序”,方可下載使用。

無現貨庫存之簡體書,將向海外調貨:
海外有庫存之書籍,等候約45個工作天;
海外無庫存之書籍,平均作業時間約60個工作天,然不保證確定可調到貨,尚請見諒。

為了保護您的權益,「三民網路書店」提供會員七日商品鑑賞期(收到商品為起始日)。

若要辦理退貨,請在商品鑑賞期內寄回,且商品必須是全新狀態與完整包裝(商品、附件、發票、隨貨贈品等)否則恕不接受退貨。

優惠價:87 392
絕版無法訂購

暢銷榜

客服中心

收藏

會員專區