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arXiv · 2307.10202

Modules for Leavitt path algebras of bi-separated graphs via representations graphs

Raimund Preusser
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Abstract

Leavitt path algebras of bi-separated graphs have been recently introduced by R. Mohan and B. Suhas. These algebras provide a common framework for studying various generalisations of Leavitt path algebras. In this paper we obtain modules for the Leavitt path algebra $L(\dot E)$ of a finitely bi-separated graph $\dot{E}=(E,C,D)$ by introducing the notion of a representation graph for $\dot{E}$. Among these modules we find a class of simple modules. If the bi-separation on $E$ is the Cuntz-Krieger bi-separation (and hence $L(\dot{E})$ is isomorphic to the usual Leavitt path algebra $L(E)$), one recovers the celebrated Chen simple modules.

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Raimund Preusser. 2023-07-13. Modules for Leavitt path algebras of bi-separated graphs via representations graphs. https://arxiv.org/abs/2307.10202

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