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 -tilting-finite algebras and give the numbers of their two-term silting objects. Finally, we explore when -tilting-finiteness implies representatoin-finiteness, and obtain several classes of algebras in which a -tilting-finite algebra is representation-finite.
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