A note about levels and sublevels of algebras obtained by the Cayley-Dickson process
Abstract
In this paper, we generalize the concepts of level and sublevel of a composition algebra to algebras obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for everyt∈ N, % \ a division algebraAt \ of dimension2t \ over the power-series fieldK\X1,X2,...,Xt\.\, \ This gives us the possibility to construct a division algebra of dimension 2t\, and prescribed level and sublevel 2k , k,\,t∈ % N* \ and a division algebra of dimension % 2t+1,t∈ N\, and prescribed level and sublevel% \,2k+1,k∈ N.\,
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