Local representation theory: Index
Local representation theory: Index
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DOI：
10.1017/cbo9780511623592
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
J. Alperin
中科院分区：
文献类型：
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作者：
J. Alperin
本文的目的是介绍有限群表示论的一些关键结果。为了使该帐户保持合理的基础性，以便可以用于研究生水平的课程，Alperin 教授将重点放在局部表示理论上，并始终强调模块理论。通过这种方式，可以相当快地获得许多深入的结果。在两章介绍性的章节之后，格林的基本结果得到了证明，这反过来又导致了布劳尔第一主定理。然后提出了布劳尔第二大定理的模块形式的证明，随后讨论了费特连接地图和格林对应关系的工作。本书最后对布劳尔-戴德理论进行了部分新颖的处理。作为一本教科书，本书包含了一个学期课程的充足材料。大多数章节的末尾都提供了练习；一些结果将在下文中使用。表示论应用于数论、组合学和代数的许多领域。对于那些对该主题本身或其应用感兴趣的人来说，这本书将是一个很好的介绍。
The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in many areas of algebra. This book will serve as an excellent introduction to those interested in the subject itself or its applications.