Anti-tori in quaternionic lattices over \(\mathbb{F}_q(t)\)

• Date: 2024
• Main Authors: Bondarenko, Ievgen, Bondarenko, Nataliia
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2024
• Subjects: anti-torus; quaternionic lattice; free subgroup; 11R52; 20F65; 20F67
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2217
• Journal Title: Algebra and Discrete Mathematics

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 \(...