On a finite state representation of \(GL(n,\mathbb{Z})\)

• Date: 2023
• Main Authors: Oliynyk, A., Prokhorchuk, V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: automorphism of rooted tree; finite state automorphism; integer matrix; free group; 20E08; 20E22; 20E26
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158
• Journal Title: Algebra and Discrete Mathematics

It is examined finite state automorphisms of regular rooted trees constructed in [6] to represent groups \(GL(n,\mathbb{Z})\).  The number of states of automorphisms that correspond to elementary matrices is computed. Using the representation of \(GL(2,\mathbb{Z})\) over an alphabet of size \(4\)  a...