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Quadratic formulas for split quaternions

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arxiv 1905.08153 v3 pith:F42LPY5Q submitted 2019-05-15 math.RA

Wensheng Cao This is my paper · ORCID
classification math.RA
keywords algebraformulasquaternionsplitzeroalgebrascomputingcontain
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abstract

Unlike the Hamilton quaternion algebra, the split-quaternions contain nontrivial zero divisors. In general speaking, it is hard to find the solutions of equations in algebras containing zero divisor. In this paper, we manage to derive explicit formulas for computing the roots of $x^{2}+bx+c=0$ in split quaternion algebra.

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  1. Quadratic Split Quaternion Polynomials: Factorization and Geometry

    math.RA 2019-08 conditional novelty 6.0 of 10

    Quadratic split quaternion polynomials factorize exactly under conditions that can be read off from intersections with the null quadric, and every such polynomial with linearly independent coefficients or vanishing no...

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