Related papers: Recurrence relations over division algebras

Polynomial relations for generators of $su(2)$ Lie algebra in arbitrary representations are found. They generalize usual relation for Pauli operators in spin 1/2 case and permit to construct modified Holstein-Primakoff transformations in…

We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the…

The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…

Ordinary orthogonal polynomials are uniquely characterized by the three term recurrence relations up to an overall multiplicative constant. We show that the newly discovered M-indexed orthogonal polynomials satisfy 3+2M term recurrence…

We derive the recurrence relations for relativistic Coulomb integrals directly from the integral representations with the help of computer algebra methods. In order to manage the computational complexity of this problem, we employ holonomic…

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…

We study the subfields of quaternion algebras that are quadratic extensions of their center in characteristic 2. We provide examples of the following: two non-isomorphic quaternion algebras that share all their quadratic subfields, two…

The paper presents a classification of quadratic extension algebras, also known as algebras of degree 2, as well as several characterizations of quaternion algebras over a field (of characteristic not 2). The presentation is not restricted…

We initiate the study of a natural generalisation of the classical Bochner-Krall problem asking which linear ordinary differential operators possess sequences of eigenpolynomials satisfying linear recurrence relations of finite length; the…

Recursive algebraic construction of two infinite families of polynomials in $n$ variables is proposed as a uniform method applicable to every semisimple Lie group of rank $n$. Its result recognizes Chebyshev polynomials of the first and…

We show that the Catalan-Schroeder convolution recurrences and their higher order generalizations can be solved using Riordan arrays and the Catalan numbers. We investigate the Hankel transforms of many of the recurrence solutions, and…

We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations…

This paper is devoted to several new results concerning (standard) octonion polynomials. The first is the determination of the roots of all right scalar multiples of octonion polynomials. The roots of left multiples are also discussed,…

Using a direct algebraic approach we derive convolution identities for second order sequences, hereby distinguishing between sequences obeying the same or different recurrence relations. We also state a general convolution for Horadam…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry…

We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are…

To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…

We introduce new algebraic structures associated with heptagon relations -- higher analogue of the well-known pentagon. The main points we deal with are: (i) polygon relations as algebraic imitations of Pachner moves, on the example of…

Colour algebras over fields of odd characteristic are well-known noncommutative Jordan algebras. We define colour algebras more generally over a unital commutative associative ring with $\frac{1}{2}\in R$, and show that colour algebras can…