Self-similarity of the classical $p$-adic Lie groups and Lie algebras
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910678253568000 |
|---|---|
| author | Livramento, Karina Noseda, Francesco |
| author_facet | Livramento, Karina Noseda, Francesco |
| contents | We exhibit infinite lists of ramification indices $δ$ for which the classical Lie groups over the ring of integers of $p$-adic fields admit a faithful self-similar action on a regular rooted $δ$-ary tree in such a way that the action is transitive on the first level. These results follow from the study of virtual endomorphisms of the classical Lie lattices over the same type of rings. In order to compute the ramification indices for all the types of groups treated in the paper, we compute the indices of principal congruence subgroups of the orthogonal groups for a class of local rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similarity of the classical $p$-adic Lie groups and Lie algebras Livramento, Karina Noseda, Francesco Group Theory 20E08, 20E18, 11E57 (Primary) 11E95, 17B20, 22E20, 22E60 (Secondary) We exhibit infinite lists of ramification indices $δ$ for which the classical Lie groups over the ring of integers of $p$-adic fields admit a faithful self-similar action on a regular rooted $δ$-ary tree in such a way that the action is transitive on the first level. These results follow from the study of virtual endomorphisms of the classical Lie lattices over the same type of rings. In order to compute the ramification indices for all the types of groups treated in the paper, we compute the indices of principal congruence subgroups of the orthogonal groups for a class of local rings. |
| title | Self-similarity of the classical $p$-adic Lie groups and Lie algebras |
| topic | Group Theory 20E08, 20E18, 11E57 (Primary) 11E95, 17B20, 22E20, 22E60 (Secondary) |
| url | https://arxiv.org/abs/2410.22639 |