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arXiv · 1701.03178

Subsets of vertices give Morita equivalences of Leavitt path algebras

Lisa Orloff Clark·Astrid an Huef·Pareoranga Luiten-Apirana
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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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Lisa Orloff Clark, Astrid an Huef, Pareoranga Luiten-Apirana. 2017-01-11. Subsets of vertices give Morita equivalences of Leavitt path algebras. https://arxiv.org/abs/1701.03178

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