Groupoids of finitely aligned higher-rank graphs via filters and graph morphisms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911159307730944 |
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| author | Clark, Lisa Orloff Jones, Malcolm |
| author_facet | Clark, Lisa Orloff Jones, Malcolm |
| contents | Path and boundary-path groupoids of finitely aligned higher-rank graphs are often constructed using either filters or graph morphisms. We generalise the graph morphism approach to finitely aligned P-graphs where (Q, P) is a weakly quasi-lattice ordered group, and we show the filter approach and the graph morphism approach yield isomorphic path and boundary-path groupoids. To do this, we define conjugacy of partial semigroup actions such that conjugate actions have isomorphic semidirect product groupoids. Combining our results with others in the literature, we survey many isomorphic presentations of path and boundary-path groupoids at different levels of generality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13929 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Groupoids of finitely aligned higher-rank graphs via filters and graph morphisms Clark, Lisa Orloff Jones, Malcolm Rings and Algebras Operator Algebras 22A22 (primary), 16W22, 46L05 (secondary) Path and boundary-path groupoids of finitely aligned higher-rank graphs are often constructed using either filters or graph morphisms. We generalise the graph morphism approach to finitely aligned P-graphs where (Q, P) is a weakly quasi-lattice ordered group, and we show the filter approach and the graph morphism approach yield isomorphic path and boundary-path groupoids. To do this, we define conjugacy of partial semigroup actions such that conjugate actions have isomorphic semidirect product groupoids. Combining our results with others in the literature, we survey many isomorphic presentations of path and boundary-path groupoids at different levels of generality. |
| title | Groupoids of finitely aligned higher-rank graphs via filters and graph morphisms |
| topic | Rings and Algebras Operator Algebras 22A22 (primary), 16W22, 46L05 (secondary) |
| url | https://arxiv.org/abs/2509.13929 |