03574nam 22005895 450 99641818890331620210419112904.03-030-35118-110.1007/978-3-030-35118-2(CKB)4920000000496058(DE-He213)978-3-030-35118-2(MiAaPQ)EBC6157923(PPN)243758405(EXLCZ)99492000000049605820210419h2020 uy 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierBasic Representation Theory of Algebras[electronic resource] /by Ibrahim Assem, Flávio U. Coelho1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (X, 311 p. 288 illus.)Graduate Texts in Mathematics,0072-5285 ;2833-030-35117-3 Includes bibliographical references and index.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 in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.Graduate Texts in Mathematics,0072-5285 ;283Associative ringsRings (Algebra)Category theory (Mathematics)Homological algebraAssociative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035Associative rings.Rings (Algebra).Category theory (Mathematics).Homological algebra.Associative Rings and Algebras.Category Theory, Homological Algebra.512.9Assem Ibrahimauthttp://id.loc.gov/vocabulary/relators/aut1020549Coelho Flávio Uauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK996418188903316Basic Representation Theory of Algebras2413546UNISA