The number of arrows in the quiver of tilting modules over a path algebra of Dynkin type.
type: Item
instance of: scholarly article
title: The number of arrows in the quiver of tilting modules over a path algebra of Dynkin type.
zbMATH Open document ID: 1303.16020
author: Ryoichi Kase
published in: Tsukuba Journal of Mathematics
publication date: 2013-07-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1101.4747
full work available at URL: https://projecteuclid.org/euclid.tkbjm/1373893409
review text: Let \(Q\) be a Dynkin quiver and let \(kQ\) be the path algebra of \(Q\), where \(k\) is an algebraically closed field. Happel and Unger defined a partial order on the set of basic tilting modules. The tilting quiver \(\overrightarrow{\mathcal K}(kQ)\) is the Hasse diagram of this partial order. The author gives formulas for the number of arrows in \(\overrightarrow{\mathcal K}(kQ)\) for any Dynkin quiver \(Q\).
reviewed by: Justyna Kosakowska
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16E30
zbMATH DE Number: 6192632
zbMATH Keywords: path algebras
zbMATH Keywords: tilting modules
zbMATH Keywords: representations of Dynkin quivers
zbMATH Keywords: numbers of arrows
MaRDI profile type: Publication
OpenAlex ID: W2245262447
arXiv ID: 1101.4747
DOI: 10.21099/TKBJM/1373893409
description: scientific article; zbMATH DE number 6192632