In this paper, we exploit the formal equivalence of the Solution Manifold of two distinct physical systems to create enough symmetries so as to characterize them by Noether Invariants, thus favoring their future quantization. In so doing, we somehow generalize the Arnold Transformation for non-necessarily linear systems. Very particularly, this algorithm applies to the case of the motion on the de Sitter space-time providing a finite-dimensional algebra generalizing the Heisenberg–Weyl algebra globally. In this case, the basic (contact) symmetry is imported from the motion of a (non-relativistic) particle on the sphere S3.

中文翻译：

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非线性系统中的共享对称性：球体 S3 外德西特时空上的广义 Heisenberg-Weyl 代数

在本文中，我们利用两个不同物理系统的解流形的形式等价性来创建足够的对称性，以便用诺特不变量来表征它们，从而有利于它们未来的量化。这样做，我们以某种方式将阿诺德变换推广到非必要的线性系统。非常特别地，该算法适用于德西特时空运动的情况，提供了一个在全局范围内推广海森堡-外尔代数的有限维代数。在这种情况下，基本（接触）对称性是从球体上（非相对论）粒子的运动中引入的小号3.