Octonionic Planes and Real Forms of G2, F4 and E6

Abstract

In this work we present a useful way to introduce the octonionic projective and hyperbolic plane through the use of Veronese vectors. Then we focus on their relation with the exceptional Jordan algebra 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, F4and E6 groups and finally give a classification of all octonionic and split-octonionic planes as symmetric spaces.

16 pages, 3 figures

References in corpus (3)

• Exceptional Lie groups
• The Standard Model, The Exceptional Jordan Algebra, and Triality
• Jordan algebras, exceptional groups, and higher composition laws

Cited by in corpus (3)

• Dixon-Rosenfeld Lines and the Standard Model
• Black hole solutions of three dimensional E${}_6$-gravity
• Collineation groups of octonionic and split-octonionic planes