A twisted group algebra structure for an algebra obtained by the Cayley – Dickson process
UDC 512.55 Starting from some ideas given in [J. W. Bales, A tree for computing the Cayley–Dickson twist, Missouri J. Math. Sci., 21, No. 2, 83–93 (2009)], in this paper we present an algorithm for computing the elements of the basis in an algebra obtained by the Cayley–Dickson process....
Збережено в:
| Дата: | 2022 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2022
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/6949 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 512.55
Starting from some ideas given in [J. W. Bales, A tree for computing the Cayley–Dickson twist, Missouri J. Math. Sci., 21, No. 2, 83–93 (2009)], in this paper we present an algorithm for computing the elements of the basis in an algebra obtained by the Cayley–Dickson process.  As a consequence of this result, we prove that an algebra obtained by the Cayley–Dickson process is a twisted group algebra for the group $G=\mathbb{Z}_{2}^{n},n=2^{t}$, $t\in \mathbb{N}$, over a field $K$ with ${\rm char} K\neq 2$.  We give some properties and applications of the quaternion nonassociative algebras.  |
|---|---|
| DOI: | 10.37863/umzh.v74i6.6949 |