A note about algebras obtained by the Cayley-Dickson process
Abstract
In this paper, we generalize the concepts of level and sublevels of a composition algebra to algebras obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for every t∈ N, a division algebra At of dimension 2t over the power-series field K\X1,X2,...,Xt\. This gives us the possibility to construct a division algebra of dimension 2t and prescribed level 2k k, t∈ N*.
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