Basic Representation Theory of Algebras (Paperback)
暫譯: 代數的基本表示理論 (平裝本)
Assem, Ibrahim, Coelho, Flávio U.
- 出版商: Springer
- 出版日期: 2022-05-10
- 售價: $2,460
- 貴賓價: 9.5 折 $2,337
- 語言: 英文
- 頁數: 311
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3030991407
- ISBN-13: 9783030991401
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相關分類:
離散數學 Discrete-mathematics
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商品描述
This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander-Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander-Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras.
Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course innon-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.
商品描述(中文翻譯)
這本教科書介紹了代數的表示理論，重點關注其兩個最重要的方面：Auslander-Reiten 理論和模範疇的根的研究。首先介紹並描述模範疇根的幾個特徵，然後呈現不可約態射和幾乎分裂序列的核心概念，接著提供 Auslander-Reiten 龍圖的定義，該龍圖編碼了模範疇的許多信息。接下來轉向自同態代數的研究，一方面導出 Auslander 代數的定義，另一方面則涉及傾斜理論。這本書以表示有限代數的選定性質作結，這是目前對代數理解最透徹的類別。
本書旨在為研究表示理論的研究生提供指導，對於任何希望學習這一快速發展領域基礎的數學家也具有興趣。讀者需具備非交換或同調代數的研究生課程背景，這在大多數大學中是標準的先修課程。
作者簡介
Ibrahim Assem obtained his PhD. from Carleton University, Canada, in 1981, and he has taught mathematics at the Université de Sherbrooke, Canada, since 1988. His main research interests are the representation theory of algebras, cluster algebras and homological algebra. He has published 115 research papers, one chapter in a collective book, four textbooks and one monograph.
Flávio Ulhoa Coelho has taught at the University of São Paulo, Brazil, since 1985. He obtained his PhD. from the University of Liverpool, UK in 1990. He has been a Full Professor since 2003 and was the director of USP's Institute of Mathematics and Statistics from 2010-2014. He has published over 70 research papers and three undergraduate textbooks in mathematics, as well as nine literature books.
作者簡介(中文翻譯)
Ibrahim Assem 於1981年獲得加拿大卡爾頓大學的博士學位，自1988年以來在加拿大舍布魯克大學教授數學。他的主要研究興趣包括代數的表示理論、叢代數和同調代數。他已發表115篇研究論文、一本合輯中的章節、四本教科書和一本專著。
Flávio Ulhoa Coelho 自1985年以來在巴西聖保羅大學任教。他於1990年獲得英國利物浦大學的博士學位。自2003年以來，他擔任正教授，並於2010年至2014年擔任聖保羅大學數學與統計學研究所的所長。他已發表超過70篇研究論文和三本本科數學教科書，以及九本文學書籍。
