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arXiv · 2311.02896

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

Gene Abrams·Efren Ruiz·Mark Tomforde
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Abstract

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 compatibility condition, implies that the Leavitt path algebras $L_k(E)$ and $L_k(F)$ are graded Morita equivalent. Along the way, we build a new type of $L_k(E)$--$L_k(F)$-bimodule (a bridging bimodule), which we use to establish the graded equivalence.

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Gene Abrams, Efren Ruiz, Mark Tomforde. 2023-11-06. Recasting the Hazrat Conjecture: Relating Shift Equivalence to Graded Morita Equivalence. https://arxiv.org/abs/2311.02896

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