有限群的表示论与结合代数 Representation Theory of Finite Groups and Associative Algebras C

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资源信息： 中文名: 有限群的表示论与结合代数 原名: Representation Theory of Finite Groups and Associative Algebras 作者: Charles W. Curtis and Irving Reiner 资源格式: DJVU 版本: 清晰版 出版社: American Mathematical Society 书号: 0821840665 发行时间: 2006年 地区: 美国 语言: 英文 概述:

内容简介: 本书概述了有限群，结合环及结合代数表示论。除了Burnside书中表示论的经典内容，本书着重叙述了诱导特征，诱导表示，拟Frobenius环，Frobenius代数，整数表示及模表示论.迄今为止。其中的许多内容仅见于研究论文中。本书注重一般方法，将理论构建于满足极小条件环上的模。为帮助研究者得到特定群的具体表示，书中包含了大量的例子以及问题，并给出了一些群表示应用于有限群结构理论的例子。 本书前三章给出了一些介绍性的材料,同时也为后续的章节提供了背景. 4-7章介绍了满足极小条件的半单环的结构理论及其在群表示与特征上的应用 4,8,9,10章介绍了满足极小条件的环及有限维代数 3,11章介绍了代数数论及群的整数表示 12章介绍了模表示论 First published in 1962, this classic book remains a remarkably complete introduction to various aspects of the representation theory of finite groups. One of its main advantages is that the authors went far beyond the standard elementary representation theory, including a masterly treatment of topics such as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations. These and many other subjects are treated extremely thoroughly, starting with basic definitions and results and proceeding to many important and crucial developments. Numerous examples and exercises help the reader of this unsurpassed book to master this important area of mathematics. 内容截图:

目录: Notation I.Background from Group Theory II.Representations and Modules III.Algebraic Number Theory IV.Semi-simple Rings and Group Algebras V.Group Characters VI.Induced Characters VII.Induced Representations VIII.Non-Semi-Simple Rings IX.Frobenius Algebras X.Splitting Fields and Separable Algebras XI.Integral Representations XII.Modular Representations Index