李群结构和李群几何
￥ 51.23 5.2折 ￥ 98 九五品
仅1件
浙江杭州
认证卖家担保交易快速发货售后保障
作者(德)Joachim Hilgert (J.希尔格特)
出版社世界图书出版公司
ISBN9787510098468
出版时间2016-05
版次1
装帧平装
开本16开
纸张胶版纸
页数744页
字数99999千字
定价98元
上书时间2024-08-03
商品详情
- 品相描述：九五品
- 商品描述
-
基本信息
书名:李群结构和李群几何
定价：98.00元
作者:(德)Joachim Hilgert (J.希尔格特)
出版社：世界图书出版公司
出版日期：2016-05-01
ISBN：9787510098468
字数：605000
页码：744
版次：1
装帧：平装
开本：16开
商品重量：
编辑推荐
《李群结构和李群几何(英文)》由世界图书出版公司北京公司出版。
内容提要
该书介绍了李群及其在流形上的作用，它受到广大数学家和学生的喜爱。 该书是在作者1991年写的教材Lie-Gruppen und Lie-Algebren 的基础上，介绍了李群的基本原理，书中增加了其过去近20年的教学和研究工作编著的，并且着重强调了微分几何在该领域中的作用。该书内容丰富， 书中大量的练习和选用的提示为学生提供了充分的学习指引。
目录
Introduction 1.1 Teaching Suggestions 1.2 Fundamental Notation Part Ⅰ Matrix Groups 2 Concrete Matrix Groups 2.1 The General Linear Group 2.2 Groups and Geometry 2.3 Quaternionic Matrix Groups 3 The Matrix Exponential Function 3.1 Smooth Functions Defined by Power Series 3.2 Elementary Properties of the Exponential Function 3.3 The Logarithm Function 3.4 The Baker—Campbell—Dynkin—Hausdorff Formula 4 Linear Lie Groups 4.1 The Lie Algebra of a Linear Lie Group 4.2 Calculating Lie Algebras of Linear Lie Groups 4.3 Polar Decomposition of Certain Algebraic Lie Groups Part Ⅱ Lie Algebras Elementary Structure Theory of Lie Algebras 5.1 Basic Concepts 5.2 Nilpotent Lie Algebras 5.3 The Jordan Decomposition 5.4 Solvable Lie Algebras 5.5 Semisimple Lie Algebras 5.6 The Theorems of Levi and Malcev 5.7 Reductive Lie Algebras 6 Root Decomposition 6.1 Cartan Subalgebras 6.2 The Classification of Simple sl2（K）—Modules 6.3 Root Decompositions of Semisimple Lie Algebras 6.4 Abstract Root Systems and Their Weyl Groups 7 Representation Theory of Lie Algebras 7.1 The Universal Enveloping Algebra 7.2 Generators and Relations for Semisimple Lie Algebras 7.3 Highest Weight Representations 7.4 Ado's Theorem 7.5 Lie Algebra Cohomology 7.6 General Extensions of Lie Algebras Part Ⅲ Manifolds and Lie Groups 8 Smooth Manifolds 8.1 Smooth Maps in Several Variables 8.2 Smooth Manifolds and Smooth Maps 8.3 The Tangent Bundle 8.4 Vector Fields 8.5 Integral Curves and Local Flows 8.6 Submanifolds 9 Basic Lie Theory 9.1 Lie Groups and Their Lie Algebras 9.2 The Exponential Function of a Lie Group 9.3 Closed Subgroups of Lie Groups and Their Lie Algebras 9.4 Constructing Lie Group Structures on Groups 9.5 Covering Theory for Lie Groups 9.6 Arcwise Connected Subgroups and Initial Subgroups 10 Smooth Actions of Lie Groups 10.1 Homogeneous Spaces 10.2 Frame Bundles 10.3 Integration on Manifolds 10.4 Invariant Integration 10.5 Integrating Lie Algebras of Vector Fields Part Ⅳ Structure Theory of Lie Groups 11 Normal Subgroups， Nilpotent and Solvable Lie Groups 11.1 Normalizers， Normal Subgroups， and Semidirect Products 11.2 Commutators， Nilpotent and Solvable Lie Groups 11.3 The Automorphism Group of a Lie Group 12 Compact Lie Groups 12.1 Lie Groups with Compact Lie Algebra 12.2 Mamal Tori in Compact Lie Groups 12.3 Linearity of Compact Lie Groups 12.4 Topological Properties 13 Semisimple Lie Groups 13.1 Cartan Decompositions 13.2 Compact Real Forms 13.3 The Iwasawa Decomposition 14 General Structure Theory 14.1 Mamal Compact Subgroups 14.2 The Center of a Connected Lie Group 14.3 The Manifold Splitting Theorem 14.4 The Exponential Function of Solvable Groups 14.5 Dense Integral Subgroups 14.6 Appendix： Finitely Generated Abelian Groups 15 Complex Lie Groups 15.1 The Universal Complefication 15.2 Linearly Complex Reductive Lie Groups 15.3 Complex Abelian Lie Groups 15.4 The Automorphism Group of a Complex Lie Group 16 Linearity of Lie Groups 16.1 Linearly Real Reductive Lie Groups 16.2 The Estence of Faithful Finite—Dimensional Represent 16.3 Linearity of Complex Lie Groups 17 Classical Lie Groups 17.1 Compact Classical Groups 17.2 Noncompact Classical Groups 17.3 More Spin Groups 17.4 Conformal Groups 18 Nonconnected Lie Groups 18.1 Extensions of Discrete Groupy Lie Groups 18.2 Coverings of Nonconnected Lie Groups 18.3 Appendix： Group Cohomology Part Ⅴ Appendices A Basic Covering Theory A.1 The Fundamental Group A.2 Coverings B Some Multilinear Algebra B.1 Tensor Products and Tensor Algebra B.2 Symmetric and Exterior Products B.3 Clifford Algebras， Pin and Spin Groups C Some Functional Analysis C.1 Bounded Operators C.2 Hilbert Spaces C.3 Compact Symmetric Operators on Hilbert Spaces D Hints to Exercises References Index
作者介绍
Joachim Hilgert (J.希尔格特)是国际知名学者，在数学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
序言
-
【封面】
— 没有更多了 —
以下为对购买帮助不大的评价