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Support $\tau $-tilting modules and recollements

Volume 167 / 2022

Xin Ma, Zongzhen Xie, Tiwei Zhao Colloquium Mathematicum 167 (2022), 303-328 MSC: 18E40, 16S90, 16G10. DOI: 10.4064/cm8358-11-2020 Published online: 28 June 2021


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 $.


  • Xin MaCollege of Science
    Henan University of Engineering
    451191 Zhengzhou, P.R. China
  • Zongzhen XieDepartment of Mathematics and Computer Science
    School of Biomedical Engineering and Informatics
    Nanjing Medical University
    211166 Nanjing, P.R. China
  • Tiwei ZhaoSchool of Mathematical Sciences
    Qufu Normal University
    273165 Qufu, P.R. China

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