English

Silting-discrete graded path algebras

Representation Theory 2026-05-25 v1

Abstract

We classify connected finite acyclic graded quivers QQ for which the graded path algebra kQkQ, regarded as a formal dg algebra, is silting-discrete. We prove that kQkQ is silting-discrete if and only if it is derived-discrete, and that both conditions are equivalent to the underlying graph of QQ being of type ADE, or of type A~\widetilde{A} with unequal clockwise and counter-clockwise total degrees. The key ingredient is an explicit construction of an infinite pre-simple-minded collection in textpvdkQ\\text{pvd } kQ in the non-discrete case.

Keywords

Cite

@article{arxiv.2605.23704,
  title  = {Silting-discrete graded path algebras},
  author = {Riku Fushimi},
  journal= {arXiv preprint arXiv:2605.23704},
  year   = {2026}
}

Comments

10 pages

R2 v1 2026-07-22T07:28:27.741Z