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

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-04-09 DOI:10.1007/s10468-024-10266-w

Gene Abrams, Efren Ruiz, Mark Tomforde

引用次数: 0

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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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

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.