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Moves on k-graphs preserving Morita equivalence

Journal Article


Abstract


  • We initiate the program of extending to higher-rank graphs (k-graphs) the geometric classification of directed graph -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, which leave invariant the Morita equivalence class of its -algebra. These moves - in-splitting, delay, sink deletion, and reduction - are inspired by the moves for directed graphs described by Sorensen (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.

Publication Date


  • 2022

Citation


  • Eckhardt, C., Fieldhouse, K., Gent, D., Gillaspy, E., Gonzales, I., & Pask, D. (2022). Moves on k-graphs preserving Morita equivalence. Canadian Journal of Mathematics, 74(3), 655-685. doi:10.4153/S0008414X21000055

Scopus Eid


  • 2-s2.0-85114253098

Web Of Science Accession Number


Start Page


  • 655

End Page


  • 685

Volume


  • 74

Issue


  • 3

Abstract


  • We initiate the program of extending to higher-rank graphs (k-graphs) the geometric classification of directed graph -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, which leave invariant the Morita equivalence class of its -algebra. These moves - in-splitting, delay, sink deletion, and reduction - are inspired by the moves for directed graphs described by Sorensen (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.

Publication Date


  • 2022

Citation


  • Eckhardt, C., Fieldhouse, K., Gent, D., Gillaspy, E., Gonzales, I., & Pask, D. (2022). Moves on k-graphs preserving Morita equivalence. Canadian Journal of Mathematics, 74(3), 655-685. doi:10.4153/S0008414X21000055

Scopus Eid


  • 2-s2.0-85114253098

Web Of Science Accession Number


Start Page


  • 655

End Page


  • 685

Volume


  • 74

Issue


  • 3