Recollements and Gorenstein projective modules for gentle algebras

Abstract

Let $A=\mathbb{k}Q/\mathcal{I}$ be a gentle algebra. We provide a bijection between non-projective indecomposable Gorenstein projective modules over $A$ and special recollements induced by an arrow $a$ on any full-relational oriented cycle $\mathcal{C}$, which satisfies some interesting properties, for example, the tensor functor $-{\otimes }_{A}A/A\epsilon A$ sends Gorenstein projective module $aA$ to an indecomposable projective $A/A\epsilon A$-module; and $-{\otimes }_{A}A/A\epsilon A$ preserves Gorenstein projective objects if any two full-relational oriented cycles do not have common vertex.

Updated some content