A note about algebras obtained by the Cayley-Dickson process

2010/01/09 by Flaut, Cristina
#17A20 #17A35 #17A45 #17A75 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1001.1440

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 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 2^k k, t∈ ℕ^*.

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