, Volume 15, Issue 1, pp 123-150

Complex algebras on n-order polynomials and generalizations of trigonometry, oscillator model and Hamilton dynamics

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Abstract.

A generator of the complex algebra within the framework of general formulation obeys the quadratic equation of the type e 2 = a 1 e − a 0. In this paper we construct the general complex algebras of the n-th order where the generators obey n-order polynomial equation of the type e n  = a n - 1 e n - 1 − a n - 2 e n - 2 + ... + (−) n + 1 a 0, with real coefficients a k ,  k = 0, 1, ... n − 1. This algebra induces a generalized trigonometry ((n + 1)-gonometry), subyacent to the n-th order oscillator model and to the n-th order Hamilton equations.