A construction of support $\tau$-tilting modules over $\tau$-tilting finite algebras
Abstract
The notion of (semi)bricks, regarded as a generalization of (semi)simple modules, appeared in a paper of Ringel in 1976. In recent years, there has been several new developments motivated by links to {\tau}-tilting theory studied by Demonet-Iyama-Jasso and Asai. In this paper, we will discuss how to glue semibricks along a recollement with the intermediate extension functor similar to gluing simple modules by Beilinson-Bernstein-Deligne. As an application, we investigate the behavior of {\tau}-tilting finite under recollements of module categories of algebras. Moreover, we give some examples to show the construction of support {\tau}-tilting modules over {\tau}-tilting finite algebras by gluing semibricks via recollements.
Keywords
Cite
@article{arxiv.1908.02245,
title = {A construction of support $\tau$-tilting modules over $\tau$-tilting finite algebras},
author = {Yingying Zhang},
journal= {arXiv preprint arXiv:1908.02245},
year = {2023}
}
Comments
accepted for publication in Adv. Math. (China)