On the representation rings of quivers of exceptional Dynkin type.
type: Item
instance of: scholarly article
title: On the representation rings of quivers of exceptional Dynkin type.
zbMATH Open document ID: 1153.16012
author: Martin Herschend
published in: Bulletin des Sciences Mathématiques
publication date: 2008-07-11T00:00:00Z
review text: In the paper the representation ring \(R(\mathbb{E}_6)\) of the Dynkin quiver \(\mathbb{E}_6\) is investigated. The representation ring \(R(Q)\) of a quiver \(Q\) encodes direct sums and tensor products of representations of the quiver \(Q\). The author presents methods which allow to reduce the computation of parts of \(R(Q)\) to the computation of \(R(Q')\) for connected subquivers \(Q'\) of \(Q\). Developing these methods the author computes and gives an explicit description of the representation ring \(R(\mathbb{E}_6)\) (for all orientations of \(\mathbb{E}_6\)). Moreover, there is explained how one can apply these methods (presented in the paper) to compute representation rings of \(\mathbb{E}_7\) and \(\mathbb{E}_8\).
reviewed by: Justyna Kosakowska
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 19A22
zbMATH DE Number: 5300470
zbMATH Keywords: exceptional Dynkin quivers
zbMATH Keywords: quiver representations
zbMATH Keywords: tensor products
zbMATH Keywords: Clebsch-Gordan problem
zbMATH Keywords: representation rings
MaRDI profile type: Publication
full work available at URL: j.bulsci.2007.11.005
OpenAlex ID: W2094279031
cites work: Lattices over curve singularities with large conductor
cites work: Algebra VIII: Representations of finite-dimensional algebras. Transl. from the Russian
cites work: On the representation ring of a quiver.
cites work: Galois coverings and the Clebsch–Gordan problem for quiver representations
cites work: Tensor products on quiver representations.
cites work: Q3997012
DOI: 10.1016/J.BULSCI.2007.11.005
Recommended article: On generic extensions of representations of a Dynkin quiver of type \(D\).
Recommended article: On generic extensions of representations of a Dynkin quiver of type \(A\).
Recommended article: On the representation ring of a quiver.
Recommended article: Abstract representation theory of Dynkin quivers of type \(A\)
Recommended article: Representations of quivers over a ring and the weak Krull-Schmidt theorems.
Recommended article: Rings of invariants for representations of quivers.
Recommended article: EXCEPTIONAL SEQUENCES FOR QUIVERS OF DYNKIN TYPE
Recommended article: Representation theory of Dynkin quivers. Three contributions
Recommended article: On the coordinate rings of quiver varieties associated to extended Dynkin diagrams
Recommended article: Degenerations for representations of extended Dynkin quivers
description: scientific article; zbMATH DE number 5300470