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群的表示与群的特征(第2版)(英文版)(Representations and Characters of Groups)

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  分類: 图书,英语与其他外语,英语读物,英文版,科普,
  品牌: 詹姆斯

基本信息·出版社:世界图书出版公司

·页码:458 页

·出版日期:2009年

·ISBN:7510004586/9787510004582

·条形码:9787510004582

·包装版本:2版

·装帧:平装

·开本:24

·正文语种:英语

·外文书名:Representations and Characters of Groups

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内容简介《群的表示与群的特征(第2版)(英文版)》内容为: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.

编辑推荐《群的表示与群的特征(第2版)(英文版)》由詹姆斯所著。

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

……[看更多目录]

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.

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群的表示与群的特征(第2版)(英文版)(Representations and Characters of Groups)

 
 
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