Levels and sublevels of division algebras obtained by the Cayley-Dickson process
Abstract
\ We generalize the concepts of level and sublevel of a composition algebra to division algebras obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for everyt∈ N, \ a nonassociative 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-\0\ and dimension \,2t\, and prescribed level \,\,2k+1 , k∈ N% -\0\,t∈ N,t≥ 2.
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