A note about levels and sublevels of algebras obtained by the\n Cayley-Dickson process

2010/06/04 by Cristina Flaut, Flaut, Cristina
Mathematics · #Algebraic and Geometric Analysis #Advanced Topics in Algebra #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1006.0944

Abstract

In this paper, thinspace thinspace we generalize the concepts of thinspace\nlevel thinspace and thinspace sublevel of a composition algebra to algebras\nobtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for\neveryt\∈ \ℕ, small % a division algebraA_t small of\ndimension2^t small over the power-series\nfieldK X₁,X₂,...,X_t . , small This gives us the possibility to\nconstruct a division algebra of thinspace dimension thinspace\n2^t , small and prescribed thinspace level and sublevel thinspace\n thinspace 2^k small , thinspace thinspacek, ,t\∈ Bbb%\nN^* small and a division algebra of thinspace dimension thinspace%\n2^t+1,t\∈ \ℕ , small and prescribed thinspace level and sublevel%\n ,2^k+1,k\∈ \ℕ. , medskip \n

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