Levels and sublevels of algebras obtained by the Cayley-Dickson process

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 every t in N, a nonassociative division algebra A_t of dimension 2^t over the power-series field K{X₁,X₂,...,X_t}. This gives us the possibility to construct a division algebra of dimension 2^t and prescribed level and sublevel 2^k, k, t in N^* and a division algebra of dimension and prescribed level and sublevel 2^k + 1, t,k in N.

levels.pdf (208K)

Cristina Flaut < cflaut@univ-ovidius.ro >