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Rigid and τ-locally free modules via Taft algebras

  • Edmund Heng
  • Calvin Pfeifer
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Abstract

We show that rigid modules are τ-locally free for a large family of 1-Iwanaga--Gorenstein algebras. This family includes many cases of the algebras introduced by Geiss--Leclerc--Schröer in their Inventiones paper "Quivers with relations for symmetrizable Cartan matrices I: Foundations", hence answering a question posed by Geiss--Leclerc--Schröer for many new cases. Our result is achieved by introducing coactions of Taft algebras and applying the recent theory developed by the first-named author and Coulembier.

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Cite

BibTeXRIS
BibTeX
@misc{heng2026rigid,
  title = {{Rigid and $τ$-locally free modules via Taft algebras}},
  author = {Edmund Heng and Calvin Pfeifer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30543},
  eprint = {2610.30543},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30543},
}
RIS
TY  - UNPB
TI  - Rigid and τ-locally free modules via Taft algebras
AU  - Edmund Heng
AU  - Calvin Pfeifer
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30543
UR  - https://arxiv.org/abs/2610.30543
AB  - We show that rigid modules are τ-locally free for a large family of 1-Iwanaga--Gorenstein algebras. This family includes many cases of the algebras introduced by Geiss--Leclerc--Schröer in their Inventiones paper "Quivers with relations for symmetrizable Cartan matrices I: Foundations", hence answering a question posed by Geiss--Leclerc--Schröer for many new cases. Our result is achieved by introducing coactions of Taft algebras and applying the recent theory developed by the first-named author and Coulembier.
ER  -