A New Geometric Morita Invariant for Higher Rank Graph $C^*$-algebras
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912863372705792 |
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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 |