On the singularities of the exponential function of a semidirect product
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913865610035200 |
|---|---|
| author | Chirvasitu, Alexandru Dahmen, Rafael Neeb, Karl-Hermann Schmeding, Alexander |
| author_facet | Chirvasitu, Alexandru Dahmen, Rafael Neeb, Karl-Hermann Schmeding, Alexander |
| contents | We show that the Fréchet--Lie groups of the form $C^{\infty}(M)\rtimes \mathbb{R}$ resulting from smooth flows on compact manifolds $M$ fail to be locally exponential in several cases: when at least one non-periodic orbit is locally closed, or when the flow restricts to a linear one on an orbit closure diffeomorphic to a torus. As an application, we prove that the Bondi--Metzner--Sachs group of symmetries of an asymptotically flat spacetime is not locally exponential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the singularities of the exponential function of a semidirect product Chirvasitu, Alexandru Dahmen, Rafael Neeb, Karl-Hermann Schmeding, Alexander Group Theory Mathematical Physics 22E65 (primary), 22E66, 58B25, 58D05, 37C05 (secondary) We show that the Fréchet--Lie groups of the form $C^{\infty}(M)\rtimes \mathbb{R}$ resulting from smooth flows on compact manifolds $M$ fail to be locally exponential in several cases: when at least one non-periodic orbit is locally closed, or when the flow restricts to a linear one on an orbit closure diffeomorphic to a torus. As an application, we prove that the Bondi--Metzner--Sachs group of symmetries of an asymptotically flat spacetime is not locally exponential. |
| title | On the singularities of the exponential function of a semidirect product |
| topic | Group Theory Mathematical Physics 22E65 (primary), 22E66, 58B25, 58D05, 37C05 (secondary) |
| url | https://arxiv.org/abs/2408.15053 |