Zixu Li, Yu Qiu, Yu Zhou
We show that the Koszul functor of a homologically smooth graded gentle algebra can be realized as the half rotation in a geometric model. As a byproduct, we prove an intersection-dim formula involving the Koszul functor.
This paper contains 7 sections, 19 theorems, 56 equations, 14 figures.
Theorem 1
For any graded open arc $\tilde{\eta}$, there is an isomorphism in $\operatorname{per}\Lambda_{\mathbf{A}}$, where $\mathrm{K}^{\mathbf{A}}$ is a quasi-inverse of $\mathrm{K}_{\mathbf{A}}$. That is, there is a commutative diagram \xymatrix@C=3pc{ \widetilde{\operatorname{CA}}(\mathbf{S}^{\lambda}) \ar[d]_{\sqrt{\varrho}} \ar[r]^{\operatorname{Y}}& \operatorname
