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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 70, Pages 4447-4454
http://dx.doi.org/10.1155/S016117120320538X

Eight-dimensional real absolute-valued algebras with left unit whose automorphism group is trivial

A. Rochdi

Département de Mathématiques et Informatique, Faculté des Sciences, Université Hassan II, BP 7955, Casablanca, Morocco

Received 5 May 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We classify, by means of the orthogonal group 𝒪7(ℝ), all eight-dimensional real absolute-valued algebras with left unit, and we solve the isomorphism problem. We give an example of those algebras which contain no four-dimensional subalgebras and characterise with the use of the automorphism group those algebras which contain one.