Moduli spaces for representations of concealed-canonical algebras
type: Item
instance of: scholarly article
title: Moduli spaces for representations of concealed-canonical algebras
zbMATH Open document ID: 1013.16006
author: Helmut Lenzing
author: Matyas Domokos
published in: Journal of Algebra
publication date: 2002-09-08T00:00:00Z
review text: The paper under review is a sequel of [\textit{M. Domokos, H. Lenzing}, J. Algebra 228, No. 2, 738-762 (2000; Zbl 0955.16015)] where the authors investigated the relative invariants and moduli spaces introduced by \textit{A. D. King} [Q. J. Math., Oxf. II. Ser. 45, No. 180, 515-530 (1994; Zbl 0837.16005)]. Let \(k\) be an algebraically closed field, let \(\Sigma\) be a finite-dimensional \(k\)-algebra, and let \(\text{mod }\Sigma\) be the category of finite-dimensional right \(\Sigma\)-modules. The authors study in detail the module category when \(\Sigma\) is a concealed-canonical algebra. In fact the class of such algebras consists of representation-infinite algebras of tame or wild representation type. They prove that for any admissible weight all the corresponding moduli spaces are isomorphic to a certain projective space. As a consequence the authors show that in the case of a tame concealed algebra any infinite moduli space for families of modules is a projective space and all fields of rational invariants on irreducible components of representation spaces are purely transcendental. In particular, a generalization of a result of \textit{C. M. Ringel} [Invent. Math. 58, 217-239 (1980; Zbl 0433.15009)] for the rational invariants of extended Dynkin quivers is obtained.
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 1797478
zbMATH Keywords: finite-dimensional algebras
zbMATH Keywords: representations
zbMATH Keywords: concealed-canonical algebras
zbMATH Keywords: tame concealed algebras
zbMATH Keywords: relative invariants
zbMATH Keywords: admissible weights
zbMATH Keywords: semistability
zbMATH Keywords: coarse moduli spaces
zbMATH Keywords: extended Dynkin quivers
zbMATH Keywords: perpendicularity
reviewed by: Aleksandr G. Aleksandrov
MaRDI profile type: Publication
full work available at URL: jabr.2001.9117
OpenAlex ID: W2026104292
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DOI: 10.1006/JABR.2001.9117
description: scientific article; zbMATH DE number 1797478