Modules for Leavitt Path Algebras of Bi-separated Graphs via Representation Graphs

Abstract

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

Keywords

Leavitt path algebra / Bi-separated graph / Simple modules / 16S88 / 16D70

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