A Journey Through Representation Theory pdf epub mobi txt 電子書下載2025

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Caroline Gruson is Professor of Mathematics at Université de Lorraine.

Vera Serganova is Professor of Mathematics at University of California, Berkeley.

出版者:Springer

作者:Caroline Gruson

出品人:

頁數:223

译者:

出版時間:2018-10-15

價格:0

裝幀:Paperback

isbn號碼:9783319982694

叢書系列:universitext

圖書標籤:

錶示論
數學

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This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field.

The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter.

Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.

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由Serganova的Math 252 notes演變而來，原名a sentimental journey through representation theory，緻敬斯特恩《多情客遊記》。主要脈絡是有限群錶示，緊群的酉錶示，還有quiver錶示，其中一部分從Zelevinsky的reps of classical finite groups: a Hopf algebra approach藉鑒很多。

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