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Endomorphism algebras of Gorenstein-projective modules over string algebras
Abstract
Let A be a string algebra. We identify its Gorenstein-projective support τ-tilting pairs with a distinguished class of maximal good collections and give a finite compatibility graph for them. Under the G-condition, we construct an explicit labelled tiled-surface model for EndA(T) for every nonzero basic Gorenstein-projective module T. Under the same condition, we show that A is representation-finite if and only if EndA(T) is representation-finite for every basic Gorenstein-projective module T.
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BibTeX
@misc{liu2026endomorphism,
title = {{Endomorphism algebras of Gorenstein-projective modules over string algebras}},
author = {Yu-Zhe Liu and Zheng Xin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00937},
eprint = {2610.00937},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00937},
}
RIS
TY - UNPB
TI - Endomorphism algebras of Gorenstein-projective modules over string algebras
AU - Yu-Zhe Liu
AU - Zheng Xin
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00937
UR - https://arxiv.org/abs/2610.00937
AB - Let A be a string algebra. We identify its Gorenstein-projective support τ-tilting pairs with a distinguished class of maximal good collections and give a finite compatibility graph for them. Under the G-condition, we construct an explicit labelled tiled-surface model for End_A(T) for every nonzero basic Gorenstein-projective module T. Under the same condition, we show that A is representation-finite if and only if End_A(T) is representation-finite for every basic Gorenstein-projective module T.
ER -