Frontiers of Mathematics in China

, Volume 11, Issue 4, pp 765–814 | Cite as

Representation theory of Dynkin quivers. Three contributions

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Abstract

The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin (and Euclidean) quivers. They should be helpful as part of a direct approach to study represen-tations of quivers, and they shed some new light on properties of Dynkin and Euclidean quivers.

Keywords

Quiver Dynkin quiver Euclidean quiver the exceptional vertices of a Dynkin quiver representations of quivers thin representations filtrations of vector spaces conical representations of star quivers Auslander-Reiten quiver thick subcategories perpendicular subcategories one-point extension antichains of a poset antichains of an additive category simplification hammocks the 2-4-8 property the magic Freudenthal-Tits square 

MSC

16G20 16G60 05E10 16D90 16G70 

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© Higher Education Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2.Department of MathematicsShanghai Jiao Tong UniversityShanghaiChina

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