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Duplication methods for embeddings of real division algebras

Department of Mathematical and Computational Sciences, University of Toronto Mississauga 3359 Mississauga Road N., Mississauga, On L5L 1C6, Canada

E-mail Address: marina.tvalavadze@utoronto.ca

Corresponding author.

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Noureddine Motya

Département de Mathématiques et Informatique, Faculté des Sciences Ben M’Sik, Université Hassan II, Casablanca 7955, Morocco

E-mail Address: noureddinemotya@gmail.com

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, and

Abdellatif Rochdi

Département de Mathématiques et Informatique, Faculté des Sciences Ben M’Sik, Université Hassan II, Casablanca 7955, Morocco

E-mail Address: abdellatifro@yahoo.fr

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https://doi.org/10.1142/S0219498822500633Cited by:3 (Source: Crossref)

Abstract

We introduce two groups of duplication processes that extend the well known Cayley–Dickson process. The first one allows to embed every $4$ -dimensional (4D) real unital algebra $𝒜$ into an 8D real unital algebra denoted by $FD (𝒜) .$ We also find the conditions on $𝒜$ under which $FD (𝒜)$ is a division algebra. This covers the most classes of known $4$ D real division algebras. The second process allows us to embed particular classes of $4$ D RDAs into $8$ D RDAs. Besides, both duplication processes give an infinite family of non-isomorphic $8$ D real division algebras whose derivation algebras contain $su (2)$ .

Communicated by L. A. Bokut

Keywords:

AMSC: 17A35, 17A36

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