群的表示与群的特征（第2版） [Representations and Characters of Groups] pdf epub mobi txt 电子书 下载 2025

简体网页||繁体网页

☆☆☆☆☆

詹姆斯（James.C.） 著

承接 住宅 自建房 室内改造 装修设计 免费咨询 QQ：624617358 一级注册建筑师 亲自为您回答、经验丰富，价格亲民。无论项目大小，都全力服务。期待合作，欢迎咨询！QQ：624617358

出版社： 世界图书出版公司

ISBN：9787510004582

版次：2

商品编码：10848647

包装：平装

外文名称：Representations and Characters of Groups

开本：24开

出版时间：2009-05-01

页数：458

正文语种：英文

内容简介

Representation theory is concerned with the ways of writing a groupas a group of matrices. Not only is the theory beautiful in its own right，but it also provides one of the keys to a proper understanding of finitegroups. For example， it is often vital to have a concrete description of aparticular group； this is achieved by finding a representation of thegroup as a group of matrices. Moreover， by studying the differentrepresentations of the group， it is possible to prove results which lieoutside the framework of representation theory. One simple example： allgroups of order p2 （where p is a prime number） are abelian； this can beshown quickly using only group theory， but it is also a consequence ofbasic results about representations.

内页插图

目录

Preface
1 Groups and homomorphisms
2 Vector spaces and linear transformations
3 Group representations
4 FG-modules
5 FG-submodules and reducibility
6 Group algebras
7 FG-homomorphisms
8 Maschke's Theorem
9 Schur's Lemma
10 Irreducible modules and the group algebra
11 More on the group algebra
12 Conjugacy classes
13 Characters
14 Inner products of characters
15 The number of irreducible characters
16 Character tables and orthogonality relations
17 Normal subgroups and lifted characters
18 Some elementary character tables
19 Tensor products
20 Restriction to a subgroup
21 Induced modules and characters
22 Algebraic integers
23 Real representations
24 Summary of properties of character tables
25 Characters of groups of order pq
26 Characters of some p-groups
27 Character table of the simple group of order 168
28 Character table of GL（2， q）
29 Permutations and characters
30 Applications to group theory
31 Burnside's Theorem
32 An application of representation theory to molecular vibration
Solutions to exercises
Bibliography
Index

前言/序言

　　We have attempted in this book to provide a leisurely introduction tothe representation theory of groups. But why should this subjectinterest you？　
　　Representation theory is concerned with the ways of writing a groupas a group of matrices. Not only is the theory beautiful in its own right，but it also provides one of the keys to a proper understanding of finitegroups. For example， it is often vital to have a concrete description of aparticular group； this is achieved by finding a representation of thegroup as a group of matrices. Moreover， by studying the differentrepresentations of the group， it is possible to prove results which lieoutside the framework of representation theory. One simple example: allgroups of order p2 （where p is a prime number） are abelian； this can beshown quickly using only group theory， but it is also a consequence ofbasic results about representations. More generally， all groups of order （p and q primes） are soluble； this again is a statement purely aboutgroups， but the best proof， due to Burnside， is an outstanding exampleof the use of representation theory. In fact， the range of applications ofthe theory extends far beyond the boundaries of pure mathematics， andincludes theoretical physics and chemistry - we describe one suchapplication in the last chapter.　The book is suitable for students who have taken first undergraduatecourses involving group theory and linear algebra. We have included twopreliminary chapters which cover the necessary background material.The basic theory of representations is developed in Chapters 3-23， andour methods concentrate upon the use of modules； although this accordswith the more modem style of algebra， in several instances our proofsdiffer from those found in other textbooks. The main results are elegantand surprising.

评分☆☆☆☆☆

送货速度快，书的质量好

评分☆☆☆☆☆

List of books Edit

评分☆☆☆☆☆

评分☆☆☆☆☆

List of books Edit

评分☆☆☆☆☆

1 The General Topology of Dynamical Systems, Ethan Akin (1993, ISBN 978-0-8218-4932-3)[1]

评分☆☆☆☆☆

送货速度快，书的质量好

评分☆☆☆☆☆

2 Combinatorial Rigidity, Jack Graver, Brigitte Servatius, Herman Servatius (1993, ISBN 978-0-8218-3801-3)

评分☆☆☆☆☆

1 The General Topology of Dynamical Systems, Ethan Akin (1993, ISBN 978-0-8218-4932-3)[1]

评分☆☆☆☆☆

4 The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Russell A. Gordon (1994, ISBN 978-0-8218-3805-1)