Moves on $k$-graphs preserving Morita equivalence
Abstract
We initiate the program of extending to higher-rank graphs (-graphs) the geometric classification of directed graph -algebras, as completed in the 2016 paper of Eilers, Restorff, Ruiz, and Sorensen [ERRS16]. To be precise, we identify four "moves," or modifications, one can perform on a -graph , which leave invariant the Morita equivalence class of its -algebra . These moves -- insplitting, delay, sink deletion, and reduction -- are inspired by the moves for directed graphs described by Sorensen [S\o13] and Bates-Pask [BP04]. Because of this, our perspective on -graphs focuses on the underlying directed graph. We consequently include two new results, Theorem 2.3 and Lemma 2.9, about the relationship between a -graph and its underlying directed graph.
Cite
@article{arxiv.2006.13441,
title = {Moves on $k$-graphs preserving Morita equivalence},
author = {Caleb Eckhardt and Kit Fieldhouse and Daniel Gent and Elizabeth Gillaspy and Ian Gonzales and David Pask},
journal= {arXiv preprint arXiv:2006.13441},
year = {2020}
}