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有限群的线性表示

Jean-Pierre Serre 世界图书出版公司
出版时间:

2008-10  

出版社:

世界图书出版公司  

作者:

Jean-Pierre Serre  

页数:

170  

Tag标签:

无  

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

章节摘录

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《有限群的线性表示》由世界图书出版公司出版。

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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。


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