Singular equivalences and Auslander-Reiten conjecture
Representation Theory
2020-11-06 v1 Rings and Algebras
Abstract
Auslander-Reiten conjecture, which says that an Artin algebra does not have any non-projective generator with vanishing self-extensions in all positive degrees, is shown to be invariant under certain singular equivalences induced by adjoint pairs, which occur often in matrix algebras, recollements and change of rings. Accordingly, several reduction methods are established to study this conjecture.
Cite
@article{arxiv.2011.02729,
title = {Singular equivalences and Auslander-Reiten conjecture},
author = {Yiping Chen and Wei Hu and Yongyun Qin and Ren Wang},
journal= {arXiv preprint arXiv:2011.02729},
year = {2020}
}
Comments
16 pages. Comments are welcome!