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Fixed points results in algebras of split quaternion and octonion. (English) Zbl 1423.11196

Summary: Fixed points of functions have applications in game theory, mathematics, physics, economics and computer science. The purpose of this article is to compute fixed points of a general quadratic polynomial in finite algebras of split quaternion and octonion over prime fields \(\mathbb Z_p\). Some characterizations of fixed points in terms of the coefficients of these polynomials are also given. Particularly, cardinalities of these fixed points have been determined depending upon the characteristics of the underlying field.

MSC:

11R52 Quaternion and other division algebras: arithmetic, zeta functions
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