Galois covering technique and tame non-simply connected posets of polynomial growth
type: Item
instance of: scholarly article
title: Galois covering technique and tame non-simply connected posets of polynomial growth
zbMATH Open document ID: 0998.16010
DOI: 10.1016/S0022-4049(98)00123-6
author: Piotr Dowbor
author: Stanisław Kasjan
published in: Journal of Pure and Applied Algebra
publication date: 2002-08-22T00:00:00Z
review text: Let \(k\) be an algebraically closed field and let \(S\) be a finite partially ordered set (poset). Let \(Q_S\) be the quiver whose vertices are the elements of \(S\) and whose arrows are described as follows: for \(x,y\in S\) there is an arrow \(x\to y\) in \(Q_S\) if and only if \(x<y\) in \(S\). The set \(S\) is said to be simply connected if so is the factor algebra of the path algebra \(kQ_S\) modulo the ideal generated by all commutativity relations [\textit{I. Assem} and \textit{A. Skowroński}, Proc. Lond. Math. Soc., III. Ser. 56, No. 3, 417-450 (1988; Zbl 0617.16018)]. The authors show that if \(S\) is not simply connected, then it is of tame prinjective type and of polynomial growth over \(k\) if and only if: (a) the Tits form of \(S\) is weakly nonnegative and (b) no subset of \(S\) belongs to one of three specific families of posets. For the terminology, the reader is referred to \textit{D. Simson} [Linear representations of partially ordered sets and vector space categories. Algebra, Logic and Applications, 4. Gordon and Breach Science Publishers, Brooklyn (1992; Zbl 0818.16009)].
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 1421591
zbMATH Keywords: finite partially ordered sets
zbMATH Keywords: tame prinjective representation type
zbMATH Keywords: simply connected posets
zbMATH Keywords: polynomial growth
zbMATH Keywords: quivers
zbMATH Keywords: path algebras
zbMATH Keywords: Tits forms
zbMATH Keywords: forbidden posets
reviewed by: Mark Kleiner
MaRDI profile type: Publication
full work available at URL: s0022-4049(98)00123-6
OpenAlex ID: W2140467076
Wikidata QID: Q131316982
description: scientific article; zbMATH DE number 1421591