A Course in Finite Group Representation Theory (Cambridge Studies in Advanced Mathematics Book 161) 1st Edition by Peter Webb (PDF)

Description

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader’s knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

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⭐エクセレントブック。何をやろうとしているか問題意識を提示しながら話を進めているので、わかりやすく内容に集中できる。具体例が必ずあり、証明も簡潔で、工夫されている。内容は古典的なものだが、その扱い方に新たな発見や見方を得る事が多い。ほんとうに良い本と思います。読んでいて楽しい。

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