---
abstract: |
    This paper was inspired by four articles: surface cluster algebras studied by Fomin-Shapiro-Thurston [@fst], the mutation theory of quivers with potentials initiated by Derksen-Weyman-Zelevinsky [@dwz], string modules associated to arcs on unpunctured surfaces by Assem-Br$\ddot{u}$stle-Charbonneau-Plamondon [@acbp] and Quivers with potentials associated to triangulated surfaces, part II: Arc representations by Labardini-Fragoso. [@lf2]. For a surface with marked points ($\Sigma,M$) Labardini-Fragoso associated a quiver with potential $(Q(\tau),S(\tau))$ then for an ideal triangulation of ($\Sigma,M$) and an ideal arc Labardini-Fragoso defined an arc representation of $(Q(\tau),S(\tau))$. This paper focuses on extent the definition of arc representation to a more general context by considering a tagged triangulation and a tagged arc. We associate in an explicit way a representation of the quiver with potential constructed Labardini-Fragoso and prove that the Jacobian relations are met.

    \
author:
- |
    Salomón Domínguez,\
    Facultad de Economía y Negocios,\
    Universidad Anáhuac Campus Sur,\
    [salomon.dominguez3@gmail.com]{}
title: Arc Representations
---

[6]{}

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