Basic Representation Theory of Algebras
1st Edition
Published on 10. May 2022
Book
Paperback/Softback
X, 311 pages
978-3-030-99140-1 (ISBN)
Description
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 in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.
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 in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.
Reviews / Votes
"This text is a well-conceived and accessible entry point to the representation theory of finite-dimensional algebras, taking the modern perspective of focussing on morphisms between modules rather than just modules themselves." (Ryan David Kinser, Mathematical Reviews, December, 2021)"This text is a well-conceived and accessible entry point to the representation theory of finite-dimensional algebras, taking the modern perspective of focussing on morphisms between modules rather than just modules themselves." (Ryan David Kinser, Mathematical Reviews, December, 2021)
More details
Product info
Paperback
Series
Edition
1st ed. 2020
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
288
288 s/w Abbildungen
X, 311 p. 288 illus.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 18 mm
Weight
493 gr
ISBN-13
978-3-030-99140-1 (9783030991401)
DOI
10.1007/978-3-030-35118-2
Schweitzer Classification
Other editions
Additional editions
Ibrahim Assem | Flávio U. Coelho
Basic Representation Theory of Algebras
Book
04/2020
1st Edition
Springer
€69.54
Shipment within 7-9 days
Persons
Ibrahim Assem obtained his PhD. from Carleton University, Canada, in 1981, and he has taught mathematics at the Universite 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.
Flavio Ulhoa Coelho has taught at the University of Sao 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.
<b>Ibrahim Assem</b> obtained his PhD. from Carleton University, Canada, in 1981, and he has taught mathematics at the Universite 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.
<b>Flavio Ulhoa Coelho</b> has taught at the University of Sao 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.
Flavio Ulhoa Coelho has taught at the University of Sao 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.
<b>Ibrahim Assem</b> obtained his PhD. from Carleton University, Canada, in 1981, and he has taught mathematics at the Universite 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.
<b>Flavio Ulhoa Coelho</b> has taught at the University of Sao 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.
Content
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.