Abelianization of the Cartwright-Steger lattice

• Datum: 2023
• Hauptverfasser: Blachar, G., Sela–Ben-David, O., Vishne, U.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2023
• Schlagworte: Bruhat-Tits affine building; Cartwright-Steger lattice; abelianization; 20E42
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1966
• Назва журналу: Algebra and Discrete Mathematics

The Cartwright-Steger lattice is a group whose Cayley graph can be identified with the Bruhat-Tits building of \(\operatorname{PGL}_d\) over a local field of positive characteristic. We give a lower bound on the abelianization of this lattice, and report that the bound is tight in all computationall...