Quiver Representations
This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is
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Ralf Schiffler
Canadian Mathematical Society Société mathématique du Canada
Quiver Representations
Canadian Mathematical Society Société mathématique du Canada Editors-in-Chief Rédacteurs-en-chef K. Dilcher K. Taylor Advisory Board Comité consultatif G. Bluman
More information about this series at http://www.springer.com/series/4318
Ralf Schiffler
Quiver Representations
123
Ralf Schiffler Department of Mathematics University of Connecticut Storrs, CT, USA
ISSN 1613-5237 ISSN 2197-4152 (electronic) ISBN 978-3-319-09203-4 ISBN 978-3-319-09204-1 (eBook) DOI 10.1007/978-3-319-09204-1 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014945363 Mathematics Subject Classification (2010): 16S70; 16G20 © Springer International Publishing Switzerland 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Céline, Ella and Christophe
Preface
This textbook is an introduction to the representation theory of finite-dimensional algebras with a strong emphasis on quivers and their representations. The book is intended to be used as a graduate textbook for a one-semester course. The first three chapters are completely self-contained, assuming only familiarity with basic notions of linear algebra, and could be used also for an ad
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