Related papers: Tetranacci and Tetranacci-Lucas Quaternions
This paper aims to introduce the $k$-Mersenne and $k$-Mersenne-Lucas octonions. We give the closed form formulae for these octonions and obtain some well-known identities like Cassini's identity, d'Ocagne's identity, Catalan identity,…
A four dimensional non-trivial extension of the Poincar\'e algebra different from supersymmetry is explicitly studied. Representation theory is investigated and an invariant Lagrangian is exhibited. Some discussion on the Noether theorem is…
Parafermions of order two are shown to be the fundamental tool to construct ternary superspaces related to cubic extensions of the Poincar\'e algebra
{\small In this paper, we find a class of division quaternion algebras over the field }$\mathbb{Q}\left( i\right) ${\small \ and a class of division symbol algebras over a cyclotomic field.}
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
Starting from known results, due to Y. Tian in [Ti; 00], referring to the real matrix representations of the real quaternions, in this paper we will investigate the left and right real matrix representations for the complex quaternions and…
The authors obtained the classification theorem for Lagrangian H-umbilical submanifolds in quaternion Euclidean spaces using the idea of quaternion extensors.
Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational…
The classic Gauss-Lucas Theorem for complex polynomials of degree $d\ge2$ has a natural reformulation over quaternions, obtained via rotation around the real axis. We prove that such a reformulation is true only for $d=2$. We present a new…
Differential calculus on the quantum quaternionic group GL(1,H$_q$) is introduced.
This paper treats certain integral lattices with respect to ternary quadratic forms, which are obtained from the data of a non-zero element and a maximal lattice in a quaternary quadratic space. Such a lattice can be described by means of…
It was proposed the Lie group such that symplectic structure of orbits of co-adjoint representation of the group is revealed symplectic structure of a rigid body dynamics in quaternion variables. It is shown that Poisson brackets of…
It is shown that the group of nonzero quaternions carries a family of natural closed Friedmann-Lema\^{\i}tre-Robertson-Walker metrics.
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried using both, the topological algebra and its central extension, which arise from the twisting of $N=2$ supersymmetry in four…
We introduce the notion of quadri-algebras. These are associative algebras for which the multiplication can be decomposed as the sum of four operations in a certain coherent manner. We present several examples of quadri-algebras: the…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
Recently, the first-named author gave a classification of 3D consistent 6-tuples of quad-equations with the tetrahedron property; several novel asymmetric 6-tuples have been found. Due to 3D consistency, these 6-tuples can be extended to…
The general linear quaternion function of degree one is a sum of terms with quaternion coefficients on the left and right. The paper considers the canonic form of such a function, and builds on the recent work of Todd Ell, who has shown…
The diagonals of a quadrilateral form four component triangles (in two ways). For each of various shaped quadrilaterals, we examine 1000 triangle centers located in these four component triangles. Using a computer, we determine when the…