有限群的线性表示

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  
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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。

用户评论 (总计9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。