Extensions in Jacobian algebras via punctured skein relations (2108.07844v2)

Abstract: Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions can be found using the tagged arcs and skein relations previously developed in cluster algebras theory. Our geometric interpretation can be used to find non-split extensions over other Jacobian algebras arising form surfaces with punctures. We show examples in type $D$ and in a punctured surface.