A New Geometric Morita Invariant for Higher Rank Graph $C^*$-algebras

Fuente: arXiv
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Hauptverfasser: Amann, Mackenzie, Gallagher, Liam, Norton, Rachael, Ruiz, Efren
Format: Preprint
Veröffentlicht: 2024
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author Amann, Mackenzie
Gallagher, Liam
Norton, Rachael
Ruiz, Efren
author_facet Amann, Mackenzie
Gallagher, Liam
Norton, Rachael
Ruiz, Efren
contents Higher rank graphs, also known as $k$-graphs, are a $k$-dimensional generalization of directed graphs and a rich source of examples of $C^*$-algebras. In the present paper, we contribute to the geometric classification program for $k$-graph $C^*$-algebras by introducing a new move on $k$-graphs, called LiMaR-split, which is a generalization of outsplit for directed graphs. We show, under one additional assumption, that LiMaR-split preserves the $k$-graph $C^*$-algebras up to Morita equivalence.
format Preprint
id arxiv_https___arxiv_org_abs_2411_19816
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A New Geometric Morita Invariant for Higher Rank Graph $C^*$-algebras
Amann, Mackenzie
Gallagher, Liam
Norton, Rachael
Ruiz, Efren
Operator Algebras
Functional Analysis
46L35, 46L05
Higher rank graphs, also known as $k$-graphs, are a $k$-dimensional generalization of directed graphs and a rich source of examples of $C^*$-algebras. In the present paper, we contribute to the geometric classification program for $k$-graph $C^*$-algebras by introducing a new move on $k$-graphs, called LiMaR-split, which is a generalization of outsplit for directed graphs. We show, under one additional assumption, that LiMaR-split preserves the $k$-graph $C^*$-algebras up to Morita equivalence.
title A New Geometric Morita Invariant for Higher Rank Graph $C^*$-algebras
topic Operator Algebras
Functional Analysis
46L35, 46L05
url https://arxiv.org/abs/2411.19816