Quiver Representations
Schiffler, Ralf
creator
author.
text
gw
Cham [u.a.]
Springer
2014
monographic
eng
pdf/application
Online-Ressource (XI, 230 p. 357 illus) online resource
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
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..
by Ralf Schiffler
Online edition Springer eBook Collection. Mathematics and Statistics
Mathematics
Algebra
Combinatorics
Mathematics
Algebra
Combinatorics
QA150-272
512
mat
CMS Books in Mathematics, Ouvrages de mathématiques de la SMC
pdf/application
9783319092041
9783319092034 (print)
http://dx.doi.org/10.1007/978-3-319-09204-1
http://zbmath.org/?q=an:1310.16015
http://dx.doi.org/10.1007/978-3-319-09204-1
http://zbmath.org/?q=an:1310.16015
141001
20180123160431.0
797793275
ger