Deformation of the Okubic Albert algebra and its relation to the Okubic affine and projective planes

Abstract

We present a deformation of the Okubic Albert algebra introduced by Elduque whose rank-1 idempotent elements are in biunivocal correspondence with points of the Okubic projective plane, thus extending to Okubic algebras the correspondence found by Jordan, Von Neumann, Wigner between the octonionic projective plane and the Albert algebra J3 (O).