Recollements and tilting modules

Abstract

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

14 pages, accepted for publication in Communications in Algebra. arXiv admin note: text overlap with arXiv:1801.02343

References in corpus (1)

• The Extension Dimension of Abelian Categories

Cited by in corpus (1)

• Recollements of extriangulated categories