English

Report on the finiteness of silting objects

Representation Theory 2023-06-22 v2 Rings and Algebras

Abstract

We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without silting object. Second, one studies two classes of τ\tau-tilting-finite algebras and give the numbers of their two-term silting objects. Finally, we explore when τ\tau-tilting-finiteness implies representatoin-finiteness, and obtain several classes of algebras in which a τ\tau-tilting-finite algebra is representation-finite.

Keywords

Cite

@article{arxiv.2002.08534,
  title  = {Report on the finiteness of silting objects},
  author = {Takuma Aihara and Takahiro Honma and Kengo Miyamoto and Qi Wang},
  journal= {arXiv preprint arXiv:2002.08534},
  year   = {2023}
}

Comments

15 pages, the proof of Theorem 4.11 revised, reference added

R2 v1 2026-06-23T13:47:36.904Z