Subsets of vertices give Morita equivalences of Leavitt path algebras

2017/01/11 by Lisa Orloff Clark, Clark, Lisa Orloff, Astrid an Huef +3 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1701.03178

openalex publication_date 2017/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that every subset of vertices of a directed graph E gives a Morita equivalence between a subalgebra and an ideal of the associated Leavitt path algebra. We use this observation to prove an algebraic version of a theorem of Crisp and Gow: certain subgraphs of E can be contracted to a new graph G such that the Leavitt path algebras of E and G are Morita equivalent. We provide examples to illustrate how desingularising a graph, and in- or out-delaying of a graph, all fit into this setting.

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• Classification and Ideal Lattices of Leavitt Path Algebras

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