Related papers: On some Grassmannians carrying an even Clifford st…
In this note, we give a list of all non-isomorphic quasitriangular structures on the 8-dimension Kac algebra K_8.
The classification of isoparametric hypersurfaces in spheres with four or six different principal curvatures is still not complete. In this paper we develop a structural approach that may be helpful for a classification. Instead of working…
Any oriented 4-dimensional real vector bundle is naturally a line bundle over a bundle of quaternion algebras. In this paper we give an account of modules over bundles of quaternion algebras, discussing Morita equivalence, characteristic…
Using quaternions and octonions, we construct some maps from the Grassmannian of 2-dimensional planes of $\mathbb{R}^n$, $\mathrm{Gr}_2(\mathbb{R}^n)$, to the projective space $\mathbb{R}\mathrm{P}^k$, for certain values of $n$ and $k$. All…
In a long series of works, it has been demonstrated, that the {\it spin-charge-family} theory offers the explanation for all in the {\it standard model} assumed properties of the second quantized fermion and boson fields, offering several…
This paper classifies Hermitian structures on 6-dimensional nilmanifolds M=G/L for which the fundamental 2-form is d d-bar closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such J is…
Given a Yamaguchi nonrigid parabolic model geometry $(G,P)$ with $G$ simple of real rank at least $3$, we use techniques developed by Erickson to establish the existence of closed, nonflat, essential, regular, normal Cartan geometries…
We clarify quasi-Frobenius configurations of finite Morley rank. 1. We remove one assumption in an identification theorem by Zamour while simplifying the proof. 2. We show that a strongly embedded quasi-Frobenius configuration of odd type,…
We explain how structures related to octonions are ubiquitous in M-theory. All the exceptional Lie groups, and the projective Cayley line and plane appear in M-theory. Exceptional G_2-holonomy manifolds show up as compactifying spaces, and…
In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice-versa.
Let $L$ be the language of rings. We provide an axiomatization of the $L$-theories of quaternions and octonions and characterize their models: they coincide, up to isomorphism, with quaternion and octonion algebras over a real closed field,…
I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss…
Nebe, Rains and Sloane studied the polynomial invariants for real and complex Clifford groups and they relate the invariants to the space of complete weight enumerators of certain self-dual codes. The purpose of this paper is to show that…
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…
We classify pseudo parallel proper CR-submanifolds in a non-flat complex space form with CR-dimension greater than one. With this result, the non-existence of recurrent as well as semi parallel proper CR-submanifolds in a non-flat complex…
The Carroll algebra is constructed as the $c\to0$ limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null…
In this paper we study regular irreducible algebraic monoids over $\fldc$ equipped with the euclidean topology. It is shown that, in such monoids, the Green classes and the spaces of idempotents in the Green classes all have natural…
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…
We present an introduction to the geometry of higher order vector and co--vector bundles (including higher order generalizations of the Finsler geometry and Kaluza--Klein gravity) and review the basic results on Clifford and spinor…
We obtain defining equations of the smooth equivariant compactification of the Grassmannian of the complex associative $3$-planes in $\C^7$, which is the parametrizing variety of all quaternionic subalgebras of the algebra of complex…