Representation Theory of Artin Algebras (Cambridge Studies in Advanced Mathematics, Series Number 36) by Maurice Auslander (PDF)

Description

This book serves as a comprehensive introduction to the representation theory of Artin algebras, a branch of algebra. Written by three distinguished mathematicians, it illustrates how the theory of almost split sequences is utilized within representation theory. The authors develop several foundational aspects of the subject. For example, the representations of quivers with relations and their interpretation as modules over the factors of path algebras is discussed in detail. Thorough discussions yield concrete illustrations of some of the more abstract concepts and theorems. The book includes complete proofs of all theorems and numerous exercises. It is an invaluable resource for graduate students and researchers.

User’s Reviews

Editorial Reviews: Review “Here is the book you may have been waiting for for a long time, maybe for fifteen years: a general introduction to the new representation theory of finite-dimensional algebras….One has to be grateful to the authors for a competent and readable introduction to the subject….The book can be recommended without reservation! It surely will serve as a standard reference.” Claus Michael Ringel, Bulletin of the American Mathematical Society Book Description This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐artin代数が、点と向きのついた矢印のグラフの表現と一致するというquiverの話を使って、artin環上の有限生成加群の直既約因子の集合を調べるためにAR-quiverというものを考察していきます。それらを考察する過程でも、圏同値の話やalmost split seaqenceなどの話題が出てきて、artin環上の加群のさまざまな性質を勉強することができます。paper backで手が出やすくなっています。

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