The Gorenstein-projective modules over a monomial algebra

We introduce the notion of a perfect path for a monomial algebra. We classify indecomposable non-projective Gorenstein-projective modules over the given monomial algebra via perfect paths. We apply the classification to a quadratic monomial algebra and describe explicitly the stable category of its...

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Bibliographic Details
Published inProceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 148; no. 6; pp. 1115 - 1134
Main Authors Chen, Xiao-Wu, Shen, Dawei, Zhou, Guodong
Format Journal Article
LanguageEnglish
Published Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.12.2018
Cambridge University Press
Subjects
Algebra
Modules
16E65
monomial algebra
quadratic monomial algebra
Nakayama algebra
Gorenstein-projective module
perfect path
16G10
18G25
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Summary:We introduce the notion of a perfect path for a monomial algebra. We classify indecomposable non-projective Gorenstein-projective modules over the given monomial algebra via perfect paths. We apply the classification to a quadratic monomial algebra and describe explicitly the stable category of its Gorenstein-projective modules.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210518000185