A peak reduction functor for socle projective representations
type: Item
instance of: scholarly article
title: A peak reduction functor for socle projective representations
zbMATH Open document ID: 0904.16008
author: Stanisław Kasjan
author: Daniel Simson
published in: Journal of Algebra
publication date: 1998-11-05T00:00:00Z
review text: The authors study representations of \(r\)-peak finite posets, namely of those posets with \(r\) maximal elements. The representations considered mainly by the authors are socle projective modules and prinjective modules over the incidence algebra of the given poset. Recall that a module \(X\) is called prinjective if the kernel of the map from the projective cover of \(X\) to \(X\) is a semisimple projective module. For posets with at most 2 peaks, a characterization of tame prinjective type has been discussed by Nazarova and the authors, respectively, but for posets with arbitrary number of maximal elements, this is an open question. Keeping this in mind, the authors associate with any poset \(J\) and a maximal element \(q\) a socle projective algebra \(A\), and provide a functor from the category of all socle projective representations of \(J\) to the category of all socle projective modules over \(A\). They call this functor a peak reduction functor and show as main result of the paper that a peak reduction functor is always full, dense and preserves and reflects tame representation type. Moreover, some special posets \(J\) are investigated in detail.
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 16D40
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 1014031
zbMATH Keywords: partially ordered sets
zbMATH Keywords: socle projective modules
zbMATH Keywords: vector space categories
zbMATH Keywords: representations of posets
zbMATH Keywords: prinjective modules
zbMATH Keywords: incidence algebras
zbMATH Keywords: tame representation type
zbMATH Keywords: peak reduction functors
reviewed by: Changchang Xi
MaRDI profile type: Publication
full work available at URL: jabr.1997.6749
OpenAlex ID: W2044195858
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DOI: 10.1006/JABR.1997.6749
Wikidata QID: Q131317016
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description: scientific article; zbMATH DE number 1014031