Symmetric quiver settings with a regular ring of invariants
type: Item
instance of: scholarly article
title: Symmetric quiver settings with a regular ring of invariants
zbMATH Open document ID: 1020.15029
DOI: 10.1016/S0024-3795(02)00407-X
author: Raf Bocklandt
published in: Linear Algebra and its Applications
publication date: 2003-05-25T00:00:00Z
review text: The author classifies all the symmetric quivers and corresponding dimension vectors having a smooth space of semisimple representation classes. The result the author obtains is that such quivers can be decomposed as a connected sum of a few number of basic quivers. Section 2 is the study of the ring of invariants. In Section 3 the author reviews briefly the Luna-Slice theorem and indicates in what way the author will use it to obtain the classification. In Section 4 the author determines some necessary conditions for a quiver setting to be coregular. In Section 5 the author determines all coregular quiver settings with two or three vertices. After that the author combines them to bigger quivers in order to construct all symmetric quiver settings that are coregular.
Mathematics Subject Classification ID: 15A72
zbMATH DE Number: 1915478
zbMATH Keywords: quiver representation
zbMATH Keywords: invariant theory
zbMATH Keywords: symmetric quivers
zbMATH Keywords: ring of invariants
zbMATH Keywords: Luna-Slice theorem
zbMATH Keywords: coregular quiver settings
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915478