Dominant dimensions, derived equivalences and tilting modules
Abstract
The Nakayama conjecture states that an algebra of infinite dominant dimension should be self-injective. Motivated by understanding this conjecture in the context of derived categories, we study dominant dimensions of algebras under derived equivalences induced by tilting modules, specifically, the infinity of dominant dimensions under tilting procedure. We first give a new method to produce derived equivalences from relatively exact sequences, and then establish relationships and lower bounds of dominant dimensions for derived equivalences induced by tilting modules. Particularly, we show that under a sufficient condition the infinity of dominant dimensions can be preserved by tilting, and get not only a class of derived equivalences between two algebras such that one of them is a Morita algebra in the sense of Kerner-Yamagata and the other is not, but also the first counterexample to a question whether generalized symmetric algebras are closed under derived equivalences.
Cite
@article{arxiv.1503.02385,
title = {Dominant dimensions, derived equivalences and tilting modules},
author = {Hongxing Chen and Changchang Xi},
journal= {arXiv preprint arXiv:1503.02385},
year = {2017}
}
Comments
28 pages. The only change in this version is that the original section 3 is divided into two parts, in order to make the structure of the paper more reasonable