On the Wakamatsu tilting conjecture
Representation Theory
2025-07-28 v3
Abstract
Let R be an associative ring with identity. We establish that the generalized Auslander-Reiten conjecture implies the Wakamatsu tilting conjecture. Furthermore, we prove that any Wakamatsu tilting R-module of finite projective dimension that is tensorly faithful is projective. By utilizing this result, we show the validity of the Wakamatsu tilting conjecture for R in two cases: when R is a left Artinian local ring or when it is the group ring of a finite group G over a commutative Artinian ring.
Cite
@article{arxiv.2407.06353,
title = {On the Wakamatsu tilting conjecture},
author = {Kamran Divaani-Aazar and Ali Mahin Fallah and Massoud Tousi},
journal= {arXiv preprint arXiv:2407.06353},
year = {2025}
}
Comments
to appear in the Journal of Archiv der Mathematik