Unipotent orbits of elements in a quaternion ring of odd order
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912785652252672 |
|---|---|
| author | Dolžan, David |
| author_facet | Dolžan, David |
| contents | Let $n \in \NN$ and let $q=p^r$ be an odd prime power. Let $R$ be a finite commutative local principal ring of cardinality $q^{n}$ with $R/J(R) \simeq GF(q)$. We study the conjugation action of the group of all unipotent elements in the quaternion ring $H(R)$ on $H(R)$ and we classify the resulting unipotent similarity classes, using a reduction to the ring of $2$-by-$2$ matrices over $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unipotent orbits of elements in a quaternion ring of odd order Dolžan, David Rings and Algebras 16P10, 16H05, 16N40, 11R52 Let $n \in \NN$ and let $q=p^r$ be an odd prime power. Let $R$ be a finite commutative local principal ring of cardinality $q^{n}$ with $R/J(R) \simeq GF(q)$. We study the conjugation action of the group of all unipotent elements in the quaternion ring $H(R)$ on $H(R)$ and we classify the resulting unipotent similarity classes, using a reduction to the ring of $2$-by-$2$ matrices over $R$. |
| title | Unipotent orbits of elements in a quaternion ring of odd order |
| topic | Rings and Algebras 16P10, 16H05, 16N40, 11R52 |
| url | https://arxiv.org/abs/2512.20341 |