有限群的线性表示 [Linear Representations of Finite Groups] 下载 mobi epub pdf 电子书 2025

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内容简介

　　《有限群的线性表示》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。《有限群的线性表示》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。《有限群的线性表示》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。

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目录

Part Ⅰ
Representations and Characters
1 Generalities on linear representations
1.1 Definitions
1.2 Basic examples
1.3 Submpmsentations
1.4 Irreducible representations
1.5 Tensor product of two representations
1.6 Symmetric square and alternating square

2 Character theory
2.1 The character of a representation
2.2 Schurs lemma; basic applications
2.3 0rthogonality relations 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
5.2 The group
5.3 The dihedral group
5.4 The group
5.5 The group
5.6 The group
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; Mackeys criterion
7.1 Induction
7.2 The character of an induced representation;
the reciprocity formula
7.3 Restriction to subgroups
7.4 Mackeys irreducibility criterion

8 Examples of induced representations
8. l Normal subgroups; applications to the degrees of the
ineducible representations
8.2 Semidirect products by an ahelian group
8.3 A review of some classes of finite groups
8.4 Syiows theorem
8.5 Linear representations of superselvable groups

9 Artins theorem
9.1 The ring R(G)
9.2 Statement of Artins 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 Brauers theorem

11 Applications of Brauers theorem
11.1 Characterization of characters
11.2 A theorem of Frobenius
11.3 A converse to Brauers theorem
11.4 The spectrum of A R(G)

12 Rationality questions
12.1 The rings RK(G) and RK(G)
12.2 Schur indices
12.3 Realizability over cyclotomic fields
12.4 The rank of RK(G)
12.5 Generalization of Artins theorem
12.6 Generalization of Brauers theorem
12.7 Proof of theorem 28

13 Rationality questions： examples
13. I The field Q
13.2 The field R
Bibliography： Part Ⅱ

Part Ⅲ
Introduction to Brauer Theory
14 The groups RK(G)， R(G)， and Pk(G)
14.1 The rings RK(G) and R，(G)
14.2 The groups Pk(G) and P^(G)
14.3 Structure of Pk(G)
14.4 Structure of PA(G)
14.5 Dualities
14.6 Scalar extensions

15 The cde triangle
15.1 Definition of c： Pk(G) ——Rk(G)
15.2 Definition of d： Rs(G) —— Rk(G)
15.3 Definition of e： Pk(G) —— RK(G)
15.4 Basic properties of the cde triangle
15.5 Example： p-gmups
15.6 Example： p-groups
15.7 Example： products ofp-groups and p-groups

16 Theorems
16.1 Properties of the cde triangle
16.2 Characterization of the image of e
16.3 Characterization of projective A [G ]-modules
by their characters
16.4 Examples of projective A [G ]-modules： irreducible
representations of defect zero

17 Proofs
17. I Change of groups
17.2 Brauers theorem in the modular case
17.3 Proof of theorem 33
17.4 Proof of theorem 35
17.5 Proof of theorem 37
17.6 Proof of theorem 38

18 Modular characters
18.1 The modular character of a representation
18.2 Independence of modular characters
18.3 Reformulations
18.4 A section ford
18.5 Example： Modular characters of the symmetric group
18.6 Example： Modular characters of the alternating group

19 Application to Artin representations
19.1 Artin and Swan representations
19.2 Rationality of the Artin and Swan representations
19.3 An invariant

Appendix
Bibliography： Part Ⅲ
Index of notation
Index of terminology

前言/序言

　　This book consists of three parts， rather different in level and purpose：
　　The first part was originally written for quantum chemists. It describes the correspondence， due to Frobenius， between linear representations and characters. This is a fundamental result， of constant use in mathematics as well as in quantum chemistry or physics. I have tried to give proofs as elementary as possible， using only the definition of a group and the rudiments of linear algebra.The examples (Chapter 5) have been chosen from those useful to chemists.

有限群的线性表示 [Linear Representations of Finite Groups] 下载 mobi epub pdf txt 电子书 格式

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书很不错，价格合理，送货很快啊。

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法国的思想家罗兰·巴特说过这样一件有趣的事：高中男生、脱衣舞观众、推理小说迷和哲学家，他们都有着相同的人生。

评分☆☆☆☆☆

挺好的，字都看的清楚。

评分☆☆☆☆☆

法国的思想家罗兰·巴特说过这样一件有趣的事：高中男生、脱衣舞观众、推理小说迷和哲学家，他们都有着相同的人生。

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例如n维射影几何的群就是n维射影空间的对称群(n+1阶矩阵群,取和标量矩阵的商)。该仿射群是保持所选的无穷远超平面不变(映射集合到自身，不是固定每一点)的子群。这个子群有一个已知的结构(n阶矩阵群和平移子群的准直积)。这个表述告诉我们什么性质是'仿射的'。用欧氏平面几何术语，平行就是:仿射变换总是将一个平行四边形变成另一个平行四边形。而圆不是仿射地，因为仿射剪切可以把圆变成椭圆。

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给娃娃囤书中 好好学习 天天向上

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要精确的解释仿射和欧氏几何之间的关系，我们要在仿射群中点出欧氏几何的群。欧氏群实际上是(采用前面仿射群的表述)正交(旋转和反射)群和平移群的准直积。

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书很不错，价格合理，送货很快啊。

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一个例子: 可定向 (也就是说，反射是除外的)椭圆几何 (也就是,把n球面相对点等同的曲面)和可定向 球面几何 (同样的非欧几何，但是相对的点没有等同起来)有同构的自同构群，偶数n的SO(n+1)。这两个看起来不同。但是事实上，这两个几何紧密相关，以一种可以精确描述的方式。

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