International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 70, Pages 4447-4454
doi:10.1155/S016117120320538X

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

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.