Quiver Mutation and Oriented Exchange Graphs

We define mutation(s) on a quiver Q. The exchange graph of Q is determined by all other quivers obtained from it via successive mutations. We show a way to orient the edges to obtain an ordered exchange graph (OEG). If the OEG is finite, it is a lattice isomorphic to Tors(kQ/I), where I is an ideal of relations determined by the cycles of Q. We mostly focus on examples of type A and oriented cycles.

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Date published: Wednesday, April 15, 2026