Support $\tau$-tilting modules and recollements

Abstract

Let $(\mbox{mod} Λ',\mbox{mod} Λ,\mbox{mod} Λ'')$ be a recollement of abelian categories for artin algebras ${\Lambda }^{\prime }$, $\Lambda$ and ${\Lambda }^{\prime \prime }$. Under certain conditions, we present an explicit construction of gluing of (support) $\tau$-tilting modules in $\mbox{mod} Λ$ with respect to (support) $\tau$-tilting modules in $\mbox{mod} Λ'$ and $\mbox{mod} Λ''$ respectively; conversely, we study the construction of (support) $\tau$-tilting modules in $\mbox{mod} Λ'$ and $\mbox{mod} Λ''$ obtained from (support) $\tau$-tilting modules in $\mbox{mod} Λ$.

26 pages, accepted for publication in Colloquium Mathematicum

References in corpus (1)

• Reduction of wide subcategories and recollements