English

A construction of support $\tau$-tilting modules over $\tau$-tilting finite algebras

Representation Theory 2023-05-09 v2

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)