Quiver Representations by Ralf SchifflerMaterial type: TextLanguage: English Series: CMS Books in Mathematics, Ouvrages de mathématiques de la SMCPublisher: Cham [u.a.] Springer 2014Description: Online-Ressource (XI, 230 p. 357 illus) online resourceContent type: Text Media type: Computermedien Carrier type: Online-RessourceISBN: 9783319092041; 9783319092034 (print)Subject(s): Mathematics | Algebra | Combinatorics | Mathematics | Algebra | CombinatoricsDDC classification: 512 LOC classification: QA150-272Other classification: mat Online resources: ZZ Volltext | Zentralblatt MATH Inhaltstext
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Part I: Quivers and their representationsRepresentations 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
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