The Albert algebra of generic matrices

We show that the Albert algebra of generic matrices is an Albert division algebra over its centroid and a pure second Tits construction. It contains a cyclic cubic subfield if and only if this holds true for every Albert division algebra over any extension of the base field.

(This paper has appeared in Comm. Algebra 27 (1999), 3703-3717)

Holger P. Petersson <Holger.Petersson@FernUni-Hagen.de>