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

有限群的线性表示 [Linear Representations of Finite Groups] epub pdf mobi txt 电子书 下载 2024

有限群的线性表示 [Linear Representations of Finite Groups] epub pdf mobi txt 电子书 下载 2024


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出版社: 世界图书出版公司
ISBN:9787506292597
版次:1
商品编码:10096494
包装:平装
外文名称:Linear Representations of Finite Groups
开本:24开
出版时间:2008-10-01
用纸:胶版纸
页数:170
正文语种:英语

有限群的线性表示 [Linear Representations of Finite Groups] epub pdf mobi txt 电子书 下载 2024



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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。

内页插图

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] epub pdf mobi txt 电子书 下载 2024

有限群的线性表示 [Linear Representations of Finite Groups] 下载 epub mobi pdf txt 电子书 2024

有限群的线性表示 [Linear Representations of Finite Groups] pdf 下载 mobi 下载 pub 下载 txt 电子书 下载 2024

有限群的线性表示 [Linear Representations of Finite Groups] mobi pdf epub txt 电子书 下载 2024

有限群的线性表示 [Linear Representations of Finite Groups] epub pdf mobi txt 电子书 下载
想要找书就要到 静思书屋
立刻按 ctrl+D收藏本页
你会得到大惊喜!!

读者评价

评分

对于一个几何和它的群,群的一个元素有时叫做该几何的一个运动。例如,可以通过基于双曲运动的一个发展来学习双曲几何的庞加莱半平面模型。

评分

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。

评分

书很好,也很便宜,做活动时买的,大师之作

评分

serre的经典著作啊 买了读一读

评分

更多值得注意的例子产生于物理学中。 正确时间的洛伦兹群,对于n ≥ 3的情况。但是这些显然是不同的几何。这里,有些有趣的结果从物理学中进来。已经证明这三个几何中的任何一个中的物理模型是对于某些模型对偶的。

评分

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。

评分

绝对经典的一本书

评分

绝对经典的一本书

评分

好书 清晰易读 值得推荐

有限群的线性表示 [Linear Representations of Finite Groups] epub pdf mobi txt 电子书 下载 2024

类似图书 点击查看全场最低价

有限群的线性表示 [Linear Representations of Finite Groups] epub pdf mobi txt 电子书 下载 2024


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