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Cohen-Macaulay truncated path and Nakayama algebras

  • Takahiro Honma
  • Satoshi Usui
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Abstract

This paper characterizes Cohen-Macaulay algebras in the sense of Auslander and Reiten [Progr. Math. 95(1991)] within the following two classes of finite dimensional algebras: (i) truncated path algebras and (ii) Nakayama algebras. For the former, our characterization in terms of ordinary quivers shows that if a Cohen-Macaulay truncated path algebra Λ is connected, then Λ or D(Λ) gives a dualizing module, where D denotes the standard duality. For the latter, we show that every Cohen-Macaulay Nakayama algebra Λ is Iwanaga-Gorenstein. In particular, Λ always gives a dualizing module. Consequently, there is no non-trivial Cohen-Macaulay algebra among truncated path and Nakayama algebras.

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Cite

BibTeXRIS
BibTeX
@misc{honma2026cohenmacaulay,
  title = {{Cohen-Macaulay truncated path and Nakayama algebras}},
  author = {Takahiro Honma and Satoshi Usui},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15386},
  eprint = {2610.15386},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15386},
}
RIS
TY  - UNPB
TI  - Cohen-Macaulay truncated path and Nakayama algebras
AU  - Takahiro Honma
AU  - Satoshi Usui
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15386
UR  - https://arxiv.org/abs/2610.15386
AB  - This paper characterizes Cohen-Macaulay algebras in the sense of Auslander and Reiten [Progr. Math. 95(1991)] within the following two classes of finite dimensional algebras: (i) truncated path algebras and (ii) Nakayama algebras. For the former, our characterization in terms of ordinary quivers shows that if a Cohen-Macaulay truncated path algebra Λ is connected, then Λ or D(Λ) gives a dualizing module, where D denotes the standard duality. For the latter, we show that every Cohen-Macaulay Nakayama algebra Λ is Iwanaga-Gorenstein. In particular, Λ always gives a dualizing module. Consequently, there is no non-trivial Cohen-Macaulay algebra among truncated path and Nakayama algebras.
ER  -