Skip to main content
placeholder image

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 $C^*$-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 $k$-graph

    $\Lambda$, which leave invariant the Morita equivalence class of its

    $C^*$-algebra $C^*(\Lambda)$. 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

    $k$-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


  • 2020

Citation


  • Eckhardt, C., Fieldhouse, K., Gent, D., Gillaspy, E., Gonzales, I., & Pask, D. (2020). Moves on $k$-graphs preserving Morita equivalence. Retrieved from http://arxiv.org/abs/2006.13441v1

Web Of Science Accession Number


Abstract


  • We initiate the program of extending to higher-rank graphs ($k$-graphs) the

    geometric classification of directed graph $C^*$-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 $k$-graph

    $\Lambda$, which leave invariant the Morita equivalence class of its

    $C^*$-algebra $C^*(\Lambda)$. 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

    $k$-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


  • 2020

Citation


  • Eckhardt, C., Fieldhouse, K., Gent, D., Gillaspy, E., Gonzales, I., & Pask, D. (2020). Moves on $k$-graphs preserving Morita equivalence. Retrieved from http://arxiv.org/abs/2006.13441v1

Web Of Science Accession Number