Pointwise-relatively-compact subgroups and trivial-weight-free representations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918071086612480 |
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| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | A pointwise-elliptic subset of a topological group is one whose elements all generate relatively-compact subgroups. A connected locally compact group has a dense pointwise-elliptic subgroup if and only if it is an extension by a compact normal subgroup of a semidirect product $\mathbb{L}\rtimes \mathbb{K}$ with connected, simply-connected Lie $\mathbb{L}$, compact Lie $\mathbb{K}$, with the commutator subgroup $\mathbb{K}'$ acting on the Lie algebra $Lie(\mathbb{L})$ with no trivial weights. This extends and recovers a result of Kabenyuk's, providing the analogous classification with $\mathbb{G}$ assumed Lie connected, topologically perfect, with no non-trivial central elliptic elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pointwise-relatively-compact subgroups and trivial-weight-free representations Chirvasitu, Alexandru Group Theory General Topology Representation Theory 22E15, 54D30, 22D05, 22D12, 22E25, 22E60, 54E52, 17B05 A pointwise-elliptic subset of a topological group is one whose elements all generate relatively-compact subgroups. A connected locally compact group has a dense pointwise-elliptic subgroup if and only if it is an extension by a compact normal subgroup of a semidirect product $\mathbb{L}\rtimes \mathbb{K}$ with connected, simply-connected Lie $\mathbb{L}$, compact Lie $\mathbb{K}$, with the commutator subgroup $\mathbb{K}'$ acting on the Lie algebra $Lie(\mathbb{L})$ with no trivial weights. This extends and recovers a result of Kabenyuk's, providing the analogous classification with $\mathbb{G}$ assumed Lie connected, topologically perfect, with no non-trivial central elliptic elements. |
| title | Pointwise-relatively-compact subgroups and trivial-weight-free representations |
| topic | Group Theory General Topology Representation Theory 22E15, 54D30, 22D05, 22D12, 22E25, 22E60, 54E52, 17B05 |
| url | https://arxiv.org/abs/2506.18861 |