03421nam 22006735 450 991029998530332120200630035834.03-319-09204-910.1007/978-3-319-09204-1(CKB)3710000000228700(SSID)ssj0001354263(PQKBManifestationID)11893700(PQKBTitleCode)TC0001354263(PQKBWorkID)11322467(PQKB)11471164(DE-He213)978-3-319-09204-1(MiAaPQ)EBC5595881(PPN)181353431(EXLCZ)99371000000022870020140904d2014 u| 0engurnn#008mamaatxtccrQuiver Representations /by Ralf Schiffler1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (XI, 230 p. 357 illus.)CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,1613-5237Bibliographic Level Mode of Issuance: Monograph3-319-09203-0 Includes bibliographical references and index.Part I: Quivers and their representations -- Representations of quivers -- Projective and injective representations -- Examples of Auslander-Reiten quivers -- Part II: Path algebras -- Algebras and modules -- Bound quiver algebras -- New algebras from old -- Auslander-Reiten theory -- Quadratic forms and Gabriel’s theorem.This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,1613-5237AlgebraAssociative ringsRings (Algebra)Combinatorial analysisAlgebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Combinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Algebra.Associative rings.Rings (Algebra)Combinatorial analysis.Algebra.Associative Rings and Algebras.Combinatorics.512Schiffler Ralfauthttp://id.loc.gov/vocabulary/relators/aut721259MiAaPQMiAaPQMiAaPQBOOK9910299985303321Quiver representations1409834UNINA