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Thick subcategories over weakly symmetric algebras with radical cube zero

  • Kaito Kimura
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Abstract

In this paper, we study thick subcategories of the (stable) module categories of finite-dimensional weakly symmetric algebras with radical cube zero. When the spectral radius of the Ext matrix is two, thick subcategories containing the algebra, equivalently thick subcategories of the stable category, are classified by Serre subcategories of a certain abelian category; when it is not two, only the trivial thick subcategories occur. As an application, this yields, to the best of our knowledge, the first examples of commutative Noetherian Gorenstein dominant local rings that are not complete intersections.

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Cite

BibTeXRIS
BibTeX
@misc{kimura2026thick,
  title = {{Thick subcategories over weakly symmetric algebras with radical cube zero}},
  author = {Kaito Kimura},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05781},
  eprint = {2609.05781},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05781},
}
RIS
TY  - UNPB
TI  - Thick subcategories over weakly symmetric algebras with radical cube zero
AU  - Kaito Kimura
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.05781
UR  - https://arxiv.org/abs/2609.05781
AB  - In this paper, we study thick subcategories of the (stable) module categories of finite-dimensional weakly symmetric algebras with radical cube zero. When the spectral radius of the Ext matrix is two, thick subcategories containing the algebra, equivalently thick subcategories of the stable category, are classified by Serre subcategories of a certain abelian category; when it is not two, only the trivial thick subcategories occur. As an application, this yields, to the best of our knowledge, the first examples of commutative Noetherian Gorenstein dominant local rings that are not complete intersections.
ER  -