Basic Representation Theory of Algebras

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

Highlights the interplay between Auslander-Reiten theory and the radical of the module category

Offers detailed examples and concrete computations that support its approach

Can be covered in a one-semester course while also being comprehensive

Inhaltsverzeichnis

Introduction.- Chapter 1: Modules, algebras and quivers.- Chapter 2: The radical and almost split sequences.- Chapter 3: Constructing almost split sequences.- Chapter 4: The Auslander-Reiten quiver of an algebra.- Chapter 5: Endomorphism algebras.- Chapter 6: Representation-finite algebras.- Bibliography.- Index.

Details

Erscheinungsjahr:	2020
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	x 311 S. 288 s/w Illustr. 311 p. 288 illus.
ISBN-13:	9783030351175
ISBN-10:	3030351173
Sprache:	Englisch
Einband:	Gebunden
Autor:	Coelho, Flávio U. Assem, Ibrahim
Auflage:	1st edition 2020
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 24 mm
Von/Mit:	Flávio U. Coelho (u. a.)
Erscheinungsdatum:	04.04.2020
Gewicht:	0,653 kg

Artikel-ID: 117548388