Quiver Representations

Softcover Nachdruck of the original 1. Auflage 2014
ISBN: 978-3-319-36317-2
Verlag: Springer International Publishing

Buch, Englisch, 230 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 3752 g

Reihe: CMS Books in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Schiffler, Ralf

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

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.

Über Autor(innen)

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