We interpret the elements of the exceptional Lie algebra e 8 (− 24) as objects in the
Standard Model, including lepton and quark spinors with the usual properties, the Standard …

We give a new construction of the Lie algebra of type E 8, in terms of 3× 3 matrices, such that
the Lie bracket has a natural description as the matrix commutator. This leads to a new …

The fermionic fields of one generation of the Standard Model (SM), including the Lorentz
spinor degrees of freedom, can be identified with components of a single real 64 …

We decompose the Lie algebra e 8 (− 24) into representations of e 7 (− 25)⊕ sl (2, R) using
our recent description of e 8 in terms of (generalized) 3× 3 matrices over pairs of division …

In his study on the geometry of Lie groups, Rosenfeld postulated a strict relation between all
real forms of exceptional Lie groups and the isometries of projective and hyperbolic spaces …

We present three new coset manifolds named Dixon-Rosenfeld lines that are similar to
Rosenfeld projective lines except over the Dixon algebra\(\mathbb {C}\otimes\mathbb …

We present a Veronese formulation of the octonionic and split-octonionic projective and
hyperbolic planes. This formulation of the incidence planes highlights the relationship …

Supermanifolds provide a very natural ground to understand and handle supersymmetry
from a geometric point of view; supersymmetry in d= 3, 4, 6, and 10 dimensions is also …

We discuss 𝒩= 1 Klein and Klein-conformal superspaces in D=(2, 2) space-time dimensions,
realizing them in terms of their functor of points over the split composition algebra ℂ s. We …

The concept of a special linear group SL (2, K) SL (2, K) with K= 𝕆 K=\mathbb {O} the
octonions does not literally make sense, due to the failure of the octonions to be an …