Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\)
An anti-torus in a CAT(0) group is a subgroup \(\langle a,b\rangle\), where \(a\) and \(b\) do not have commuting powers. We study anti-tori in quaternionic lattices \(\Gamma_\tau\) over the field \(\mathbb{F}_q(t)\) introduced by Stix-Vdovina (2017). We determine when every pair of generators of \(...
Збережено в:
| Дата: | 2024 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2024
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2217 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-2217 |
|---|---|
| record_format |
ojs |
| spelling |
oai:ojs.admjournal.luguniv.edu.ua:article-22172024-06-27T08:42:43Z Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) Bondarenko, Ievgen Bondarenko, Nataliia anti-torus, quaternionic lattice, free subgroup 11R52, 20F65, 20F67 An anti-torus in a CAT(0) group is a subgroup \(\langle a,b\rangle\), where \(a\) and \(b\) do not have commuting powers. We study anti-tori in quaternionic lattices \(\Gamma_\tau\) over the field \(\mathbb{F}_q(t)\) introduced by Stix-Vdovina (2017). We determine when every pair of generators of \(\Gamma_\tau\) generates an anti-torus, and establish the existence of \(a,b\in\Gamma_\tau\) such that the subgroup \(\langle a^{p^n},b^{p^n}\rangle\) is not abelian and not free for all \(n\geq 0\). Explicit examples of matrices \(a,b\in SL_3(\mathbb{F}_q(t))\) with this property are given. Lugansk National Taras Shevchenko University 2024-06-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2217 10.12958/adm2217 Algebra and Discrete Mathematics; Vol 37, No 2 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2217/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2217/1155 Copyright (c) 2024 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2024-06-27T08:42:43Z |
| collection |
OJS |
| language |
English |
| topic |
anti-torus quaternionic lattice free subgroup 11R52 20F65 20F67 |
| spellingShingle |
anti-torus quaternionic lattice free subgroup 11R52 20F65 20F67 Bondarenko, Ievgen Bondarenko, Nataliia Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| topic_facet |
anti-torus quaternionic lattice free subgroup 11R52 20F65 20F67 |
| format |
Article |
| author |
Bondarenko, Ievgen Bondarenko, Nataliia |
| author_facet |
Bondarenko, Ievgen Bondarenko, Nataliia |
| author_sort |
Bondarenko, Ievgen |
| title |
Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title_short |
Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title_full |
Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title_fullStr |
Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title_full_unstemmed |
Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\) |
| title_sort |
anti-tori in quaternionic lattices over \(\mathbb{f}_q(t)\) |
| description |
An anti-torus in a CAT(0) group is a subgroup \(\langle a,b\rangle\), where \(a\) and \(b\) do not have commuting powers. We study anti-tori in quaternionic lattices \(\Gamma_\tau\) over the field \(\mathbb{F}_q(t)\) introduced by Stix-Vdovina (2017). We determine when every pair of generators of \(\Gamma_\tau\) generates an anti-torus, and establish the existence of \(a,b\in\Gamma_\tau\) such that the subgroup \(\langle a^{p^n},b^{p^n}\rangle\) is not abelian and not free for all \(n\geq 0\). Explicit examples of matrices \(a,b\in SL_3(\mathbb{F}_q(t))\) with this property are given. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2024 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2217 |
| work_keys_str_mv |
AT bondarenkoievgen antitoriinquaternioniclatticesovermathbbfqt AT bondarenkonataliia antitoriinquaternioniclatticesovermathbbfqt |
| first_indexed |
2024-06-28T04:03:55Z |
| last_indexed |
2024-06-28T04:03:55Z |
| _version_ |
1811048693082619904 |