Yingying Zhang
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 τ-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 τ-tilting finite under recollements of module categories of algebras. Moreover, we give some examples to show the construction of support τ-tilting modules over τ-tilting finite algebras by gluing semibricks via recollements.