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arXiv · 1908.02245

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

Yingying Zhang
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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.

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Yingying Zhang. 2019-08-06. A construction of support $\tau$-tilting modules over $\tau$-tilting finite algebras. https://arxiv.org/abs/1908.02245

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