Classification of connected proper pairs in the affine transformation group

Fuente: arXiv
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Main Author: Miyauchi, Shunsuke
Format: Preprint
Published: 2026
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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