Representations of quivers via reflection functors

2008/04/09 by Henning Krause, Krause, Henning · 4 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum many-body systems #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0804.1428

openalex publication_date 2008/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These are the notes for a course on representations of quivers for second year students in Paderborn in summer 2007. My aim was to provide a basic introduction without using any advanced methods. It turns out that a good knowledge of linear algebra is sufficient for proving Gabriel's theorem. Thus we classify the quivers of finite representation type and study their representations using reflection functors. Further material has been added after giving this course in Bielefeld in summer 2010. This includes a discussion of regular representations and wild phenomena. In particular, two classical examples are covered: representations of the Kronecker quiver and representations of the Klein four group.

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• Abstract representation theory via coherent Auslander-Reiten diagrams
• Higher symmetries in abstract stable homotopy theories
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