English

A note on the $m$-extended module categories of Nakayama algebras

Representation Theory 2026-01-22 v1

Abstract

We study the extended module category m-modΛm\operatorname{-mod}\Lambda of an algebra Λ\Lambda, recently introduced by Gupta and Zhou. The existence of a postprojective component of m-modΛm\operatorname{-mod}\Lambda is shown for certain algebras Λ\Lambda, and a knitting algorithm through cohomological dimension vectors is provided. In particular, the extended module category of Nakayama algebras with homogeneous relations are investigated, and it is classified when they are of finite type. The paper give fully calculated AR-quivers for several Nakayama algebras.

Keywords

Cite

@article{arxiv.2601.14843,
  title  = {A note on the $m$-extended module categories of Nakayama algebras},
  author = {Endre Sørmo Rundsveen},
  journal= {arXiv preprint arXiv:2601.14843},
  year   = {2026}
}