13 citations · 41 across the 26 of their papers we have counts for
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Okubo algebras and Exceptional Periodicity: tetracode gradings, root-lattice obstructions and Clifford cones
Alessio Marrani, Daniele Corradetti
The Okubo algebra brings together ternary gradings, integral root frames and rank-three geometry. We examine how these structures extend to the complex Exceptional Periodicity alge…
Integral Orders for the Okubo Algebra and Idempotent Geometries of the Lattice
Daniele Corradetti, Alessio Marrani
We study the Coxeter-Dickson order as a common integral support for the octonionic, para-octonionic and compact real Okubo products. The three algebra structures have the sam…
Non-crystallographic systems of integers over composition algebras
Daniele Corradetti
In this work we revisit classical systems of integers inside the real normed division algebras from the point of view of finite norm shells and root systems. Building on the icosia…
Integral elements of Okubo algebra and the E8-lattice
Daniele Corradetti
In this work we study the interplay between the Coxeter-Dickson -order, the para-octonions, and the real Okubo algebra. We first explain why a usual rotation presentation of…
Recovering Composition Algebras from 3D Geometric Algebras
Daniele Corradetti
Generalized Hurwitz theorem states that there are fifteen composition algebras for any given field: seven unital, six para-unital, and two non-unital algebras. In this article we e…
Collineation groups of octonionic and split-octonionic planes
Daniele Corradetti, Alessio Marrani, Francesco Zucconi
We present a Veronese formulation of the octonionic and split-octonionic projective and hyperbolic planes. This formulation of the incidence planes highlights the relationship betw…
All Hurwitz Algebras from 3D Geometric Algebras
Daniele Corradetti, Richard Clawson, Klee Irwin
Hurwitz algebras are unital composition algebras widely known in algebra and mathematical physics for their useful applications. In this paper, inspired by works of Lesenby and Hit…
A minimal and non-alternative realisation of the Cayley plane
Daniele Corradetti, Alessio Marrani, Francesco Zucconi
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 a novel…
Jordan algebras over icosahedral cut-and-project quasicrystals
Daniele Corradetti, David Chester, Raymond Aschheim +1
In this paper we present a general setting for aperiodic Jordan algebras arising from icosahedral quasicrystals that are obtainable as model sets of a cut-and-project scheme with a…
Three Fibonacci-Chain Aperiodic Algebras
Daniele Corradetti, David Chester, Raymond Aschheim +1
Aperiodic algebras are infinite dimensional algebras with generators corresponding to an element of the aperiodic set. These algebras proved to be an useful tool in studying elemen…
A magic approach to octonionic Rosenfeld spaces
Alessio Marrani, Daniele Corradetti, David Chester +2
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…
Deformation of the Okubic Albert algebra and its relation to the Okubic affine and projective planes
Daniele Corradetti, Alessio Marrani, Francesco Zucconi
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 p…
Octonionic Planes and Real Forms of G2, F4 and E6
Daniele Corradetti, Alessio Marrani, David Chester +1
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 excep…
A Geometrical Interpretation of Okubo Spin Group
Daniele Corradetti, Francesco Zucconi
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 alge…