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The classification, up to a center-affinity, of the homogeneous quadraticdifferential systems defined on $\mathbb{R}^{3}$ that have at least asemisimple derivation with one-dimensional kernel, is achieved. It is provedthat there exist 35 families of affine equivalence classes of such systems.

Classification of Quadratic Differential Systems on $\mathbb{R}^{3}$ Having a Semisimple Derivation with a one-Dimensional Kernel