@article{Boboescu_Flaut_2022, title={A twisted group algebra structure for an algebra obtained by the Cayley – Dickson process}, volume={74}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6949}, DOI={10.37863/umzh.v74i6.6949}, abstractNote={<p>UDC 512.55</p> <p>Starting from some ideas given in [J. W. Bales, <em>A tree for computing the Cayley–Dickson twist</em>, Missouri J. Math. Sci., <strong>21</strong>, 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.<span class="Apple-converted-space"> </span>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 ${\rm char} K
eq 2$.<span class="Apple-converted-space"> </span>We give some properties and applications of the quaternion nonassociative algebras. </p>}, number={6}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Boboescu, R. and Flaut, C.}, year={2022}, month={Jul.}, pages={752 - 760} }