Support $\tau $-tilting modules and recollements
Volume 167 / 2022
Colloquium Mathematicum 167 (2022), 303-328
MSC: 18E40, 16S90, 16G10.
DOI: 10.4064/cm8358-11-2020
Published online: 28 June 2021
Abstract
Let $(\operatorname{mod} \Lambda ’,\operatorname{mod} \Lambda ,\operatorname{mod} \Lambda ”)$ be a recollement of abelian categories for artin algebras $\Lambda ’$, $\Lambda $ and $\Lambda ”$. Under certain conditions, we present an explicit construction of gluing of (support) $\tau $-tilting modules in $\operatorname{mod} \Lambda $ with respect to (support) $\tau $-tilting modules in $\operatorname{mod} \Lambda ’$ and $\operatorname{mod} \Lambda ”$ respectively. On the other hand, we study the construction of (support) $\tau $-tilting modules in $\operatorname{mod} \Lambda ’$ and $\operatorname{mod} \Lambda ”$ obtained from (support) $\tau $-tilting modules in $\operatorname{mod} \Lambda $.
