有限群的线性表示

所属分类:数学  
出版时间:2008-10   出版时间:世界图书出版公司   作者:Jean-Pierre Serre   页数:170  
Tag标签:数学,表示论,GTM,代数,Algebra,经典,Math  

前言

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.

内容概要

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。

作者简介

作者:(法国)赛尔 (Serre.J.P)

书籍目录

Part
ⅠRepresentations
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
IPart
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
products
by
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

Introduction
to
Brauer
TheoryAppendixBibliography:Part
ⅢIndex
of
notationIndex
of
terminology

章节摘录

插图:

编辑推荐

《有限群的线性表示》由世界图书出版公司出版。

图书封面

图书标签Tags

数学,表示论,GTM,代数,Algebra,经典,Math


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用户评论 (总计29条)

 
 

  •     有限群表示论最经典的书。
  •     有一点群论的基础都可以读的,很基础
  •     Serre的经典之作
  •     GTM丛书之一,值得收藏、研读。。。
  •     J.P.Serre的书,值得信赖
  •     书很好,就是字感觉有点小,质量不错
  •     经典教材,不错的书.
  •     这本群表示论的书写得非常精彩。Serre的书一直以简洁明了著称,这就是其中的典型。Serre从最简单的复数域上的有限维表示讲起,一直讲到了Grothendieck的一些理论。
  •     serre的水平毋庸置疑,据说他研究问题的思路如泉水一般清晰,值得拜读一下。
  •     黄仁宇的大历史学说,卓越的购物品质一流。本书非常精美
  •     不过现在已经很难有那样的心境去看这样的小说了。,书皮都掉了
  •     很适合学生阅读,但是这么便宜不好意思给五分以下的
  •     首先要看自己对生命、对信仰、对文学的态度如何。。,比较了好久才选中这款的
  •     中国最早的博弈论。,谋略三十六计。
  •     但是需要认真用心去读,到底是名著啊
  •     不过里面还是有点文言看不懂,挺难懂的书
  •     对考托福阅读很有帮助,庄子主要是对人生的思考
  •     和简爱有的一拼,陆续一套买全了
  •     但不适合快速学习。,令无数的人废寝忘食的看值得一看
  •     国外的教材编的不错。,书的包装跟纸质都很好。不过书的插图真的很随意
  •     精彩。。。。。。,这本买来送表弟的。08 年自己也买过一本。性价比很高的一本书
  •     内容比较新颖了,一堆书买回来
  •     《蒙田随笔》永远是我心灵的导向与慰籍,现在这本书版本很多
  •     挺好!,现在看来也觉有趣。
  •     儿时读过的优秀作品,这是一系列的一本
  •     就怕这种出了前卷,帮别人买得
  •     评论来迟,可是第五版还是公认的经典~!
  •     张爱玲的书总是让人爱不释手,适合静下心来看
  •     无法乱作评价,这本书我看了很多遍
 

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