Quasi-cluster algebras were defined in 2015 by Dupont and Palesi and are an analogous of cluster algebras for non-orientable surfaces. In this talk, we will first give an introduction on these quasi-cluster algebras and list some of their properties (finite-type classification, skein relations, among others). Then, we will associate a quiver with potential to triangulations of non-orientable surfaces and study the algebra given by this. More precisely, we use the cluster category associated to an orientable double cover of our non-orientable surface to give a correspondence between quasi-triangulations of a non-orientable surface and an analogue of cluster-tilting objects.
Joint work with Aaron Chan and Kayla Wright