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

2023/07/13 by Raimund Preusser, Preusser, Raimund
Materials Science · Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Lanthanide and Transition Metal Complexes #Operator Algebras (math.OA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2307.10202

openalex publication_date 2023/07/13 · openalex created_date 2023/07/22 · openalex updated_date 2026/07/28

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( E) of a finitely bi-separated graph E=(E,C,D) by introducing the notion of a representation graph for 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(E) is isomorphic to the usual Leavitt path algebra L(E)), one recovers the celebrated Chen simple modules.

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