English

ICE-closed subcategories and epibricks over one-point extensions

Representation Theory 2024-01-12 v1

Abstract

Let BB be the one-point extension algebra of AA by an AA-module MM. We proved that every ICE-closed subcategory inmodA\mod A can be extended to be some ICE-closed subcategories inmodB\mod B.In the same way, every epibrick in modA\mod A can be extended to be some epibricks in modB\mod B.The number of ICE-closed subcategories in modB\mod B and the number of ICE-closed subcategories in modA\mod A are denoted respectively as mm, nn.We can conclude the following inequality:m2nm \geq 2n This is the analogical in epibricks.As an application, we can get some wide τ\tau-tilting modules of BB by wide τ\tau-tilting modules of AA.

Keywords

Cite

@article{arxiv.2401.05645,
  title  = {ICE-closed subcategories and epibricks over one-point extensions},
  author = {Xin Li and Hanpeng Gao},
  journal= {arXiv preprint arXiv:2401.05645},
  year   = {2024}
}

Comments

10 pages

R2 v1 2026-06-28T14:13:53.860Z