Classification of connected proper pairs in the affine transformation group
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908772928061440 |
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| author | Miyauchi, Shunsuke |
| author_facet | Miyauchi, Shunsuke |
| contents | Let $(L, H)$ be closed subgroups of a locally compact group $G$. The pair $(L, H)$ is said to be proper if the action of $L$ on the homogeneous space $G/H$ is proper.
We give a complete list of connected closed proper pairs in the affine transformation group of $\mathbb{R}^2$. This result extends Kobayashi's classification (1992) of connected closed subgroups of the affine transformation group of $\mathbb{R}^2$acting properly on $\mathbb{R}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11933 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of connected proper pairs in the affine transformation group Miyauchi, Shunsuke Group Theory Primary 57S30, Secondary 22F30 Let $(L, H)$ be closed subgroups of a locally compact group $G$. The pair $(L, H)$ is said to be proper if the action of $L$ on the homogeneous space $G/H$ is proper. We give a complete list of connected closed proper pairs in the affine transformation group of $\mathbb{R}^2$. This result extends Kobayashi's classification (1992) of connected closed subgroups of the affine transformation group of $\mathbb{R}^2$acting properly on $\mathbb{R}^2$. |
| title | Classification of connected proper pairs in the affine transformation group |
| topic | Group Theory Primary 57S30, Secondary 22F30 |
| url | https://arxiv.org/abs/2601.11933 |