We give a construction for a gentle algebra which can be associated with a triangulated orbifold with all orbifold points having order three. First, we discuss how features of the module category can be viewed on the orbifold. Chekhov and Shapiro demonstrate how to associate a generalized cluster algebra from a triangulated orbifold. We then compare the modules over this gentle algebra with the elements of the generalized cluster algebra from the same orbifold with triangulation.
This talk is based on joint work with Yadira Valdivieso.