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arXiv · 2108.07844

Extensions in Jacobian algebras via punctured skein relations

Salomon Dominguez·Ana Garcia Elsener
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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.

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Salomon Dominguez, Ana Garcia Elsener. 2021-08-17. Extensions in Jacobian algebras via punctured skein relations. https://arxiv.org/abs/2108.07844

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