Refinement of Higher-Rank Graph Reduction
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916287804866560 |
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| author | Lippert, S. Joseph |
| author_facet | Lippert, S. Joseph |
| contents | Given a row-finite, source-free, graph of rank k, we extend the definition of reduction introduced by Eckhardt et al. This constitutes a large step forward in the extension of the geometric classification of finite directed graph $C^*$-algebras presented by Eilers et al. to higher-rank graph $C^*$-algebras. This new move acts as an inverse to delay, directly extends the previous version, and provides previously undocumented Morita classes of k-graphs. In pursuit of this extension, we formalize what constitutes a higher-rank graph move. Specifically, we use this formalization as a bridge between the new geometric reasoning and the classical category theoretic construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_17156 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Refinement of Higher-Rank Graph Reduction Lippert, S. Joseph Operator Algebras Given a row-finite, source-free, graph of rank k, we extend the definition of reduction introduced by Eckhardt et al. This constitutes a large step forward in the extension of the geometric classification of finite directed graph $C^*$-algebras presented by Eilers et al. to higher-rank graph $C^*$-algebras. This new move acts as an inverse to delay, directly extends the previous version, and provides previously undocumented Morita classes of k-graphs. In pursuit of this extension, we formalize what constitutes a higher-rank graph move. Specifically, we use this formalization as a bridge between the new geometric reasoning and the classical category theoretic construction. |
| title | Refinement of Higher-Rank Graph Reduction |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2211.17156 |