Straightening Banach-Lie-group-valued almost-cocycles
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913456841555968 |
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| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | For a compact group $\mathbb{G}$ acting continuously on a Banach Lie group $\mathbb{U}$, we prove that maps $\mathbb{G}\to \mathbb{U}$ close to being 1-cocycles for the action can be deformed analytically into actual 1-cocycles. This recovers Hyers-Ulam stability results of Grove-Karcher-Ruh (trivial $\mathbb{G}$-action, compact Lie $\mathbb{G}$ and $\mathbb{U}$) and de la Harpe-Karoubi (trivial $\mathbb{G}$-action, $\mathbb{U}:=$invertible elements of a Banach algebra). The obvious analogues for higher cocycles also hold for abelian $\mathbb{U}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Straightening Banach-Lie-group-valued almost-cocycles Chirvasitu, Alexandru Group Theory Functional Analysis General Topology 22E65, 22C05, 58B25, 46E50, 20J06, 58C15, 22E66, 22D12, 39B82, 46G20, 22E41 For a compact group $\mathbb{G}$ acting continuously on a Banach Lie group $\mathbb{U}$, we prove that maps $\mathbb{G}\to \mathbb{U}$ close to being 1-cocycles for the action can be deformed analytically into actual 1-cocycles. This recovers Hyers-Ulam stability results of Grove-Karcher-Ruh (trivial $\mathbb{G}$-action, compact Lie $\mathbb{G}$ and $\mathbb{U}$) and de la Harpe-Karoubi (trivial $\mathbb{G}$-action, $\mathbb{U}:=$invertible elements of a Banach algebra). The obvious analogues for higher cocycles also hold for abelian $\mathbb{U}$. |
| title | Straightening Banach-Lie-group-valued almost-cocycles |
| topic | Group Theory Functional Analysis General Topology 22E65, 22C05, 58B25, 46E50, 20J06, 58C15, 22E66, 22D12, 39B82, 46G20, 22E41 |
| url | https://arxiv.org/abs/2401.14929 |