Recollements and tilting modules

Abstract

Let (mod Λ',mod Λ,mod Λ'') be a recollement of module categories for artin algebras $Λ'$, $Λ$ and $Λ''$. We provide a sufficient condition such that a glued torsion pair in mod Λ is tilting when the given two torsion pairs are tilting in mod Λ' and mod Λ'' respectively. Using this result, we give a construction of gluing of tilting modules in mod Λ with respect to tilting modules in mod Λ' and