A minimal and non-alternative realisation of the Cayley plane
D Corradetti, A Marrani, F Zucconi - ANNALI DELL'UNIVERSITA'DI …, 2024 - Springer
The compact 16-dimensional Moufang plane, also known as the Cayley plane, has
traditionally been defined through the lens of octonionic geometry. In this study, we present …
traditionally been defined through the lens of octonionic geometry. In this study, we present …
a “magic” approach to octonionic Rosenfeld spaces
A Marrani, D Corradetti, D Chester… - Reviews in …, 2023 - World Scientific
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 …
real forms of exceptional Lie groups and the isometries of projective and hyperbolic spaces …
Octonionic Planes and Real Forms of , and
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 …
plane OP^2 through the use of Veronese vectors. Then we focus on their relation with the …
Collineation groups of octonionic and split-octonionic planes
D Corradetti, A Marrani, F Zucconi - arXiv preprint arXiv:2311.11907, 2023 - arxiv.org
We present a Veronese formulation of the octonionic and split-octonionic projective and
hyperbolic planes. This formulation of the incidence planes highlights the relationship …
hyperbolic planes. This formulation of the incidence planes highlights the relationship …
A geometrical interpretation of Okubo Spin group
D Corradetti, F Zucconi - Journal of Geometry and Physics, 2022 - Elsevier
In this work we define, for the first time, the affine and projective plane over the real Okubo
algebra, showing a concrete geometrical interpretation of its Spin group. Okubo algebra is a …
algebra, showing a concrete geometrical interpretation of its Spin group. Okubo algebra is a …
Pl\" ucker Coordinates and the Rosenfeld Planes
J Qiu - arXiv preprint arXiv:2401.07735, 2024 - arxiv.org
The exceptional compact hermitian symmetric space EIII is the quotient $ E_6/Spin
(10)\times_ {\mathbb {Z} _4} U (1) $. We introduce the Pl\" ucker coordinates which give an …
(10)\times_ {\mathbb {Z} _4} U (1) $. We introduce the Pl\" ucker coordinates which give an …
All Hurwitz Algebras from 3D Geometric Algebras
D Corradetti, R Clawson, K Irwin - arXiv preprint arXiv:2311.02269, 2023 - arxiv.org
Hurwitz algebras are unital composition algebras widely known in algebra and
mathematical physics for their useful applications. In this paper, inspired by works of …
mathematical physics for their useful applications. In this paper, inspired by works of …