Basic Representation Theory of Algebras

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.

“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)

• 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.