International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 11, Pages 673-678
doi:10.1155/S0161171201011292
On the constructions of Tits and Faulkner: an isomorphism theorem
13200 Isanti Street, Blaine, MN 55449, USA
Received 19 December 2000
Copyright © 2001 Sudhir R. Nath. 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
Classification theory guarantees the existence of an isomorphism
between any two E8's, at least over an algebraically closed field of characteristic 0. The purpose of this paper is to construct for any Jordan algebra J of degree 3 over a field Φ of characteristic ≠2,3 an explicit isomorphism between the algebra obtained from J by Faulkner's construction and the algebra obtained from the split octonions and J by Tits construction.