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

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发表日期：

2024年4月9日

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Gene Abrams,
Efren Ruiz,
Mark Tomforde

摘要

Let E and F be finite graphs with no sinks, and k any field. We show that shift equivalence of the adjacency matrices $A_E$ $A_{E}$ and $A_F$ $A_{F}$ , together with an additional compatibility condition, implies that the Leavitt path algebras $L_k(E)$ $L_{k} (E)$ and $L_k(F)$ $L_{k} (F)$ are graded Morita equivalent. Along the way, we build a new type of $L_k(E)$ $L_{k} (E)$ – $L_k(F)$ $L_{k} (F)$ -bimodule (a bridging bimodule), which we use to establish the graded equivalence.