Related papers: Identities for third order Jacobsthal quaternions
We study the correspondence assigning the vertices of a certain quotient of the local Bruhat-Tits tree for the general linear group over a global function field, to conjugacy classes of maximal orders in some quaternion algebras. The…
For the Lucas sequence $\{U_{k}(P,Q)\}$ we discuss the identities such as the well-known Fibonacci identities. We also propose a method for obtaining identities involving recurrence sequences. With the help of which we find an interpolating…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…
Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
The purpose of the paper is to construct a new representation of dual quaternions called bi$-$periodic dual Fibonacci quaternions. These quaternions are originated as a generalization of the known quaternions in literature such as dual…
In this paper, we present a new generalization of the Lucas numbers by matrix representation using Genaralized Lucas Polynomials. We give some properties of this new generalization and some relations between the generalized order-k Lucas…
We determine some Nichols algebras that admit a non-trivial quadratic relation associated to some families of upper triangular solutions of the Yang-Baxter equation of dimension 3.
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such…
We consider Clifford algebras over the field of real or complex numbers as a quotient algebra without fixed basis. We present classification of Clifford algebra elements based on the notion of quaternion type. This classification allows us…
The various mass relations among members of quark and lepton families are given. Three mass relations for the charm, beauty, and top quark family members are given and three mass relations for the electron, muon, and tau lepton family…
In this paper, we deal with two families of third-order Jacobsthal sequences. The first family consists of generalizations of the Jacobsthal sequence. We show that the Gelin-Ces\`aro identity is satisfied. Also, we define a family of…
This is a tutorial introduction to the representation theory of SU(2) with emphasis on the occurrence of Jacobi polynomials in the matrix elements of the irreducible representations. The last section traces the history of the insight that…
In this paper, we introduce a generalization of Balancing and Balancing-Lucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties.
This paper considers the properties of Tribonacci numbers on identities, matrices, and determinants. In the first front part, we obtain several symmetric identities of Tribonacci numbers by a matrix-based approach and binomial inversion…
We present some new linear, quadratic, cubic and quartic binomial Fibonacci, Lucas and Fibonacci--Lucas summation identities.
In this paper we study special Fibonacci quaternions and special generalized Fibonacci-Lucas quaternions in quaternion algebras over finite fields.
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…