Ralf Schiffler: Quiver Representations

Cover: 9783319363172 | Quiver Representations | Ralf Schiffler | Taschenbuch | Paperback | xi

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Beschreibung

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.

Über den Autor

Ralf Schiffler is a Professor in the Department of Mathematics at the University of Connecticut.

Zusammenfassung

First textbook on representation theory which uses the quiver representations approach

Much shorter than other texts on the subject and is meant as a textbook for a one semester course

Explicit constructions of Auslander-Reiten quivers are given

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2016
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	CMS Books in Mathematics
Inhalt:	xi 230 S. 357 s/w Illustr. 230 p. 357 illus.
ISBN-13:	9783319363172
ISBN-10:	3319363174
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Schiffler, Ralf
Auflage:	Softcover reprint of the original 1st ed. 2014
Hersteller:	Springer International Publishing Springer International Publishing AG CMS Books in Mathematics
Maße:	235 x 155 x 14 mm
Von/Mit:	Ralf Schiffler
Erscheinungsdatum:	22.09.2016
Gewicht:	0,376 kg

Artikel-ID: 103163878