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We classify, by means of the orthogonal group Ã°ÂÂ’Âª7(Ã¢Â„Â), 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

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