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Quiver representations. (English) Zbl 1310.16015
CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. Cham: Springer (ISBN 978-3-319-09203-4/hbk; 978-3-319-09204-1/ebook). xi, 230 p. (2014).
This book is an elementary course for beginners in Representation Theory of Algebras. The book has two parts. In the first part the Representation Theory is studied using quivers and their representations. In an elementary way there are presented concepts of indecomposability, projective and injective representations and introduction to Auslander-Reiten theory. Presentation of this part requires only knowledge of linear algebra and it is a good text for students who want to start learning this theory.
The second part is a little more advanced. It uses the language of algebras and modules. In this part there are presented: bound quiver algebras, tilted algebras, self-injective algebras, cluster-tilted algebras, one-point extensions etc. Moreover, this part contains more advanced Auslander-Reiten theory, quadratic forms and Gabriel’s theorem. – This book is well written and it is more elementary than other available books in Representation Theory of Algebras.

MSC:
16G20 Representations of quivers and partially ordered sets
16-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
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