Representation theory of Dynkin quivers. Three contributions

doi:10.1007/s11464-016-0548-5

Front. Math. China

2016, Vol. 11

Issue (4) : 765-814 https://doi.org/10.1007/s11464-016-0548-5

SURVEY ARTICLE

Representation theory of Dynkin quivers. Three contributions

Claus Michael RINGEL^1,^2,^*(

)

¹. Fakultät für Mathematik, Universität Bielefeld, P. O. Box 100 131, D-33501 Bielefeld, Germany
². Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

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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 simplifi-cation hammocks the 2-4-8 property the magic Freudenthal-Tits square

Corresponding Author(s): Claus Michael RINGEL

Issue Date: 30 August 2016

Cite this article:

Claus Michael RINGEL. Representation theory of Dynkin quivers. Three contributions[J]. Front. Math. China, 2016, 11(4): 765-814.

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https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0548-5
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I4/765

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