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PreprintarXiv licencearXiv

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

  • Zhe Han
  • Dawei Shen
  • Jiawei Zhou
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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.

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Cite

BibTeXRIS
BibTeX
@misc{han2026resolution,
  title = {{Resolution quivers and the QF-1 property of higher Auslander Nakayama algebras}},
  author = {Zhe Han and Dawei Shen and Jiawei Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34716},
  eprint = {2610.34716},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34716},
}
RIS
TY  - UNPB
TI  - Resolution quivers and the QF-1 property of higher Auslander Nakayama algebras
AU  - Zhe Han
AU  - Dawei Shen
AU  - Jiawei Zhou
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.34716
UR  - https://arxiv.org/abs/2610.34716
AB  - 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.
ER  -