Resolution quivers and the QF-1 property of higher Auslander Nakayama algebras

We give a resolution-quiver-theoretic proof of the QF-1 conjecture of Cruz and Marczinzik for higher Auslander Nakayama algebras of positive even global dimension. The proof combines syzygy calculations in Kupisch coordinates, which show that the projective dimensions of quotients of a fixed projective module with cyclic top strictly decrease as their lengths increase, with a torsion-pair argument and Morita's criterion.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.34716
Primary Topic
Algebraic structures and combinatorial models
Type
preprint
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preprint

Resolution quivers and the QF-1 property of higher Auslander Nakayama algebras

Jiawei Zhou, Zhe Han, Dawei Shen
arXiv (Cornell University)
Algebraic structures and combinatorial models
preprint

Resolution quivers and the QF-1 property of higher Auslander Nakayama algebras

Jiawei Zhou, Zhe Han, Dawei Shen
preprint en

Abstract

We give a resolution-quiver-theoretic proof of the QF-1 conjecture of Cruz and Marczinzik for higher Auslander Nakayama algebras of positive even global dimension. The proof combines syzygy calculations in Kupisch coordinates, which show that the projective dimensions of quotients of a fixed projective module with cyclic top strictly decrease as their lengths increase, with a torsion-pair argument and Morita's criterion.

arXiv (Cornell University)
Algebraic structures and combinatorial models
DOIOpen Access PDFOpenAlex
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Resolution quivers and the QF-1 property of higher Auslander Nakayama algebras — Jiawei Zhou, Zhe Han, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS