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

Cristina Flaut

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

Rings and Algebras 2012-01-18 v2

Authors: Cristina Flaut

Abstract

In this paper, \thinspace \thinspace we generalize the concepts of \thinspace level \thinspace and \thinspace sublevel of a composition algebra to algebras obtained by the Cayley-Dickson process. In 1967, R. B. Brown constructed, for every} $t\in \Bbb{N},$ {\small % \ a division algebra} $A_{t}$ {\small \ of dimension} $2^{t}$ {\small \ over the power-series field} $K\{X_{1},X_{2},...,X_{t}\}.\,$ {\small \ This gives us the possibility to construct a division algebra of \thinspace dimension \thinspace 2} $^{t}\,$ {\small and prescribed \thinspace level and sublevel \thinspace \thinspace 2} $^{k}$ {\small ,\thinspace \thinspace} $k,\,t\in \Bbb{% N}^{*}$ {\small \ and a division algebra of \thinspace dimension \thinspace} $% 2^{t}+1,t\in \Bbb{N}\,$ {\small and prescribed \thinspace level and sublevel}% $\,2^{k}+1,k\in \Bbb{N}.\,\medskip$

Keywords

Cayley-Dickson process composition algebra level sublevel division algebra power-series field

Cite

@article{arxiv.1006.0944,
  title  = {A note about levels and sublevels of algebras obtained by the Cayley-Dickson process},
  author = {Cristina Flaut},
  journal= {arXiv preprint arXiv:1006.0944},
  year   = {2012}
}

Comments

This paper has been withdrawn by the author due to some errors. A new version will be update soon

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

Abstract

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