A note about algebras obtained by the Cayley-Dickson process

Cristina Flaut

A note about algebras obtained by the Cayley-Dickson process

Rings and Algebras 2012-01-18 v2

Authors: Cristina Flaut

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 $t\in \Bbb{N},$ a division algebra $A_{t}$ of dimension $2^{t}$ over the power-series field $K\{X_{1},X_{2},...,X_{t}\}.$ This gives us the possibility to construct a division algebra of dimension 2 $^{t}$ and prescribed level 2 $^{k}$ $k, t\in \Bbb{N}^{*}.$

Cite

@article{arxiv.1001.1440,
  title  = {A note about algebras obtained by the Cayley-Dickson process},
  author = {Cristina Flaut},
  journal= {arXiv preprint arXiv:1001.1440},
  year   = {2012}
}

Comments

This paper has been withdrawn by the author due to some errors.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

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