Subsets of vertices give Morita equivalences of Leavitt path algebras
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 outdelaying of a graph, all fit into this setting.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 DOI:
 10.48550/arXiv.1701.03178
 arXiv:
 arXiv:1701.03178
 Bibcode:
 2017arXiv170103178O
 Keywords:

 Mathematics  Rings and Algebras