A homological characterization of AF groupoids
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913083265384448 |
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| author | Steinberg, Benjamin |
| author_facet | Steinberg, Benjamin |
| contents | An ample groupoid is said to be AF if it is a directed union of compact open principal subgroupoids. In this paper, we provide a complete homological characterization of these groupoids. Specifically, we prove that an ample groupoid is AF if and only if it has homological dimension zero. More generally, we characterize groupoids of homological dimension zero over a unital ring $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01175 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A homological characterization of AF groupoids Steinberg, Benjamin Operator Algebras 20J05, 22A22 An ample groupoid is said to be AF if it is a directed union of compact open principal subgroupoids. In this paper, we provide a complete homological characterization of these groupoids. Specifically, we prove that an ample groupoid is AF if and only if it has homological dimension zero. More generally, we characterize groupoids of homological dimension zero over a unital ring $R$. |
| title | A homological characterization of AF groupoids |
| topic | Operator Algebras 20J05, 22A22 |
| url | https://arxiv.org/abs/2605.01175 |