Extensions in Jacobian algebras via punctured skein relations
Representation Theory
2025-11-24 v2 Rings and Algebras
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 and in a punctured surface.
Keywords
Cite
@article{arxiv.2108.07844,
title = {Extensions in Jacobian algebras via punctured skein relations},
author = {Salomon Dominguez and Ana Garcia Elsener},
journal= {arXiv preprint arXiv:2108.07844},
year = {2025}
}
Comments
23 pages, several pictures