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

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...

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Datum:2023
Hauptverfasser: Oliynyk, A., Prokhorchuk, V.
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2023
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Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
Beschreibung
Zusammenfassung: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 finite state  representation of the free group of rank \(2\) over binary alphabet is constructed.