03646nam 22006855 450 991029978080332120200701101138.03-319-11475-110.1007/978-3-319-11475-0(CKB)3710000000324996(SSID)ssj0001408282(PQKBManifestationID)11787297(PQKBTitleCode)TC0001408282(PQKBWorkID)11348279(PQKB)11468633(DE-He213)978-3-319-11475-0(MiAaPQ)EBC5578971(PPN)25886916X(PPN)183148991(EXLCZ)99371000000032499620141229d2015 u| 0engurnn|008mamaatxtccrIntroduction to the Representation Theory of Algebras /by Michael Barot1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (X, 179 p. 109 illus.) Bibliographic Level Mode of Issuance: Monograph3-319-11474-3 Includes bibliographical references and indexes.Matrix Problems -- Representations of Quivers -- Algebras -- Module Categories -- Elements of Homological Algebra -- The Auslander-Reiten Theory -- Knitting -- Combinatorial Invariants -- Indecomposables and Dimensions.This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations and explains the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander–Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel‘s Theorem, the trichotomy and the Theorem of Kac – all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.Associative ringsRings (Algebra)Category theory (Mathematics)Homological algebraAlgebraAssociative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035General Algebraic Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/M1106XAssociative rings.Rings (Algebra).Category theory (Mathematics).Homological algebra.Algebra.Associative Rings and Algebras.Category Theory, Homological Algebra.General Algebraic Systems.512.9Barot Michaelauthttp://id.loc.gov/vocabulary/relators/aut768297MiAaPQMiAaPQMiAaPQBOOK9910299780803321Introduction to the Representation Theory of Algebras1564850UNINA