Daniele Corradetti, Alessio Marrani, David Chester and Raymond Aschheim (2022)

In this work we present a useful way to introduce the octonionic projective and hyperbolic plane OP 2 through the use of Veronese vectors. Then we focus on their relation with the exceptional Jordan algebra J O 3 and show that the Veronese vectors are the rank-one elements of the algebra. We then study groups of motions over the octonionic plane recovering all real forms of G2, F4 and E6 groups and finally give a classification of all octonionic and split-octonionic planes as symmetric spaces.