重塑哈兹拉特猜想：移位等价性与梯度莫里塔等价性的关系

Pub Date : 2024-04-09 DOI:10.1007/s10468-024-10266-w

Gene Abrams, Efren Ruiz, Mark Tomforde

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引用次数: 0

摘要

让 E 和 F 是没有汇的有限图，k 是任意域。我们证明了邻接矩阵 \(A_E\) 和 \(A_F\) 的移位等价性，再加上一个额外的相容性条件，意味着 Leavitt 路径代数 \(L_k(E)\) 和 \(L_k(F)\) 是分级莫里塔等价的。在这个过程中，我们建立了一种新型的 \(L_k(E)\)-\(L_k(F)\)- 双模块（桥接双模块），我们用它来建立分级等价性。

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

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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