Geodesic
Moves on k-graphs preserving Morita equivalence
Canadian journal of mathematics, Tome 74 (2022) no. 3, pp. 655-685

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DOI

We initiate the program of extending to higher-rank graphs (k-graphs) the geometric classification of directed graph $C^*$-algebras, as completed in Eilers et al. (2016, Preprint). To be precise, we identify four “moves,” or modifications, one can perform on a k-graph $\Lambda $, which leave invariant the Morita equivalence class of its $C^*$-algebra $C^*(\Lambda )$. These moves—in-splitting, delay, sink deletion, and reduction—are inspired by the moves for directed graphs described by Sørensen (Ergodic Th. Dyn. Syst. 33(2013), 1199–1220) and Bates and Pask (Ergodic Th. Dyn. Syst. 24(2004), 367–382). Because of this, our perspective on k-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 k-graph and its underlying directed graph.
DOI : 10.4153/S0008414X21000055
Mots-clés : Higher-rank graphs, classification of graph C*-algebras 
Eckhardt, Caleb; Fieldhouse, Kit; Gent, Daniel; Gillaspy, Elizabeth; Gonzales, Ian; Pask, David. Moves on k-graphs preserving Morita equivalence. Canadian journal of mathematics, Tome 74 (2022) no. 3, pp. 655-685. doi: 10.4153/S0008414X21000055
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     title = {Moves on k-graphs preserving {Morita} equivalence},
     journal = {Canadian journal of mathematics},
     pages = {655--685},
     year = {2022},
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     number = {3},
     doi = {10.4153/S0008414X21000055},
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