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＜E-Book＞
Basic Representation Theory of Algebras / by Ibrahim Assem, Flávio U. Coelho
(Graduate Texts in Mathematics. ISSN:21975612 ; 283)

Edition	1st ed. 2020.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2020
Language	English
Size	X, 311 p. 288 illus : online resource
Authors	*Assem, Ibrahim author Coelho, Flávio U author SpringerLink (Online service)
Subjects	LCSH:Associative rings LCSH:Associative algebras LCSH:Algebra, Homological FREE:Associative Rings and Algebras FREE:Category Theory, Homological Algebra
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-35118-2

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