TY - JOUR
AU - R. Boboescu
AU - C. Flaut
PY - 2022/07/07
Y2 - 2022/08/19
TI - A twisted group algebra structure for an algebra obtained by the Cayley – Dickson process
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 74
IS - 6
SE - Research articles
DO - 10.37863/umzh.v74i6.6949
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6949
AB - UDC 512.55Starting 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 ${\rm char} K
eq 2$. We give some properties and applications of the quaternion nonassociative algebras.
ER -