English

The Extension dimension of syzygy module categories

Representation Theory 2026-05-08 v2

Abstract

In this paper, our primary focus is on investigating the extension dimensions of syzygy module categories associated with Artin algebras, particularly under various equivalences. We demonstrate that, for sufficiently large ii, the ii-th syzygy module categories of derived equivalent algebras exhibit identical extension dimensions. Furthermore, we establish that the extension dimension of the ii-th syzygy module category is an invariant under both stable equivalence and separable equivalence for each nonnegative integer ii.

Keywords

Cite

@article{arxiv.2405.02921,
  title  = {The Extension dimension of syzygy module categories},
  author = {Junling Zheng and Lulu Tian and Qianyu Shu},
  journal= {arXiv preprint arXiv:2405.02921},
  year   = {2026}
}