On the boundary algebras of the Jacobian algebras of the bordered marked surfaces

Abstract

Given $\sigma$ a triangulation of bordered surface with marked points and punctures $(S,M)$, we associate an ice quiver with potential $(Q_{\sigma },W_{\sigma },F)$ and define the corresponding Jacobian algebra ${\Gamma }_{\sigma }$. We show that the boundary algebra $B(\sigma )$ of ${\Gamma }_{\sigma }$ depends only on the surface $(S,M)$.

Page = 1--17

References in corpus (3)

• Calabi-Yau algebras
• Dimer models and cluster categories of Grassmannians
• Ice quivers with potential arising from once-punctured polygons and Cohen-Macaulay modules