有限群的线性表示 pdf下载

基本信息

书名:有限群的线性表示

定价：35元

作者:（法）赛尔　著

出版社：世界图书出版公司

出版日期：2008-10-01

ISBN：9787506292597

字数：

页码：170

版次：1

装帧：平装

开本：24开

商品重量：

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内容提要

本书是一部非常经典的介绍有限群线性表示的教程，原版曾多次修订重印，作者是当今法国最突出的数学家之一，他对理论数学有全面的了解，尤以著述清晰、明了闻名。本书是他写的为数不多的教科书之一，原文是法文（1971年版），后出了德译本和英译本。本书是英译本的重印本。它篇幅不大，但深入浅出的介绍了有限群的线性表示，并给出了在量子化学等方面的应用，便于广大数学、物理、化学工作者初学时阅读和参考。

目录

Part Ⅰ
Representations and Characters
1 Generalities on linear representations
　　1.1 Definitions
　　1.2 Basic examples
　　1.3 Subrepresentations
　　1.4 Irreducible representations
　　1.5 Tensor product of two representations
　　1.6 Symmetiic square and alternating square
2 Character theory
　　2.1 The character of a representation
　　2.2 Schur's lemma; basic applications
　　2.3 Orthogonality'reiations for characters
　　2.4 Decomposition of the regular representation
　　2.5 Number of irreducible representations
　　2.6 Canonical decomposition of a representation
　　2.7 Explicit decomposition of a representation
3 Subgroups, products, induced representations
　　3.1 Abelian subgroups
　　3.2 Product of two groups
　　3.3 Induced representations
4 Compact groups
　　4.1 Compact groups
　　4.2 lnvariant measure on a compact group
　　4.3 Linear representations of compact groups
5 Examples
　　5.1 The cyclic Group Cn
　　5.2 The group C
　　5.3 The dihedral group D
　　5.4 The group Dn
　　5.5 The group D
　　5.6 The group D
　　5.7 The alternating group
　　5.8 The symmetric group
　　5.9 The group of the cube
　Bibliography: Part I
Part Ⅱ　Representations in Characteristic Zero
6 The group algebra
　　6,1 Representations and modules
　　6.2 Decomposition of C[G]
　　6.3 The center of C[G]
　　6.4 Basic properties of integers
　　6.5 lntegrality properties of characters. Applications
7 Induced representations; Mackey's criterion
　　7.1 Induction
　　7.2 The character of an induced representation; the reciprocity formula
　　7.3 Restriction to subgroups
　　7.4 Mackey's irreducibility criterion
8 Examples of induced representations
　　8.1 Normal subgroups; applications to the degrees of the irreducible representations
　　8.2 Semidirect producty an abelian group
　　8.3 A review of some classes of finite groups
　　8.4 Sylow's theorem
　　8.5 Linear representations of supersolvable groups
9 Artin's theorem
　　9.1 The ring R(G)
　　9,2 Statement of Artin's theorem
　　9.3 First proof
　　9.4 Second proof of (i) (ii)
10 A theorem of Brauer
　　10.1 p-regular elements;p-elementary subgroups
　　10.2 Induced characters arising from p-elementary subgroups
　　10.3 Construction of characters
　　10.4 Proof of theorems 18 and 18'
　　10,5 Brauer's theorem
　……
part Ⅲ Introduction to Brauer Theory
Appendix
Bibliography:Part Ⅲ
Index of notation
Index of terminology

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