A twisted group algebra structure for an algebra obtained by the Cayley – Dickson process
Abstract
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.
References
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