Recasting the Hazrat Conjecture: Relating Shift Equivalence to Graded Morita Equivalence

Gene Abrams, Efren Ruiz, Mark Tomforde

Let $E$ and $F$ be finite graphs with no sinks, and $k$ any field. We show that shift equivalence of the adjacency matrices $A_E$ and $A_F$, together with an additional compatibili…