Pervasive ellipticity in locally compact groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912424814182400 |
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| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | A topological group is (openly) almost-elliptic if it contains a(n open) dense subset of elements generating relatively-compact cyclic subgroups. We classify the (openly) almost-elliptic connected locally compact groups as precisely those with compact maximal semisimple quotient and whose maximal compact subgroups act trivial-weight-freely on the Euclidean quotients of the closed derived series' successive layers. In particular, an extension of a compact connected group $\mathbb{K}$ by a connected, simply-connected solvable Lie group $\mathbb{L}$ is (openly) almost-elliptic precisely when the weights of the $\mathbb{K}$-action on $Lie(\mathbb{L})$ afforded by the extension are all non-trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pervasive ellipticity in locally compact groups Chirvasitu, Alexandru Group Theory General Topology Representation Theory 22E15, 54D30, 22D05, 22D12, 22E25, 22E60, 22E40, 17B05 A topological group is (openly) almost-elliptic if it contains a(n open) dense subset of elements generating relatively-compact cyclic subgroups. We classify the (openly) almost-elliptic connected locally compact groups as precisely those with compact maximal semisimple quotient and whose maximal compact subgroups act trivial-weight-freely on the Euclidean quotients of the closed derived series' successive layers. In particular, an extension of a compact connected group $\mathbb{K}$ by a connected, simply-connected solvable Lie group $\mathbb{L}$ is (openly) almost-elliptic precisely when the weights of the $\mathbb{K}$-action on $Lie(\mathbb{L})$ afforded by the extension are all non-trivial. |
| title | Pervasive ellipticity in locally compact groups |
| topic | Group Theory General Topology Representation Theory 22E15, 54D30, 22D05, 22D12, 22E25, 22E60, 22E40, 17B05 |
| url | https://arxiv.org/abs/2506.09642 |