Quiver Modulations and Potentials

Abstract

We introduce DWZ (Derksen-Weyman-Zelevinsky) mutation for a special class of SPs (species with potential). Generalizing a construction of Labardini-Fragoso, we associate with each triangulated, constantly weighted orbifold an SP. For such SPs the compatibility of arc flips and DWZ mutations is established. Moreover, considering not necessarily constantly weighted, unpunctured orbifolds, we define <i>colored triangulations</i> and associated SPs. Finally, we investigate and answer when the Jacobian algebras of two colored triangulations with the same underlying triangulation are isomorphic and prove that these algebras are always finite-dimensional.