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Starting from some ideas given by Bales in [Ba; 09], in this paper we presentan algorithm for computing the elements of the basis in an algebra obtained bythe Cayley-Dickson process. As a consequence of this result, we prove that analgebra obtained by the Cayley-Dickson process is a twisted group algebra forthe group G = Zn2 ; n = 2t, t 2 N, over a field K, with charK = 0. In the lastsection, we give some properties and applications of the quaternionnonassociative algebras.

A twisted group algebra structure for an algebra obtained by the Cayley-Dickson process