A field of endomorphisms R is called a Nijenhuis operator if its Nijenhuis torsion vanishes. In this work we study a specific kind of singular points of R called points of scalar type. We show that the tangent space at such points possesses a natural structure of a left-symmetric algebra (also known as pre-Lie or Vinberg-Kozul algebras). Following Weinstein's approach to linearization of Poisson structures, we state the linearisation problem for Nijenhuis operators and give an answer in terms of non-degenerate left-symmetric algebras. In particular, in dimension 2, we give classification of non-degenerate left-symmetric algebras for the smooth category and, with some small gaps, for the analytic one. These two cases, analytic and smooth, differ. We also obtain a complete classification of two-dimensional real left-symmetric algebras, which may be an interesting result on its own.

如果内同态R的扭转消失，则将其称为Nijenhuis算符。在这项工作中，我们研究R的一种特殊类型的奇异点，即标量类型的点。我们证明在这些点的切线空间拥有左对称代数（也称为前李或维伯格-科兹勒代数）的自然结构。遵循温斯坦对泊松结构线性化的方法，我们为Nijenhuis算子陈述了线性化问题，并给出了非退化左对称代数的答案。特别是，在第2维中，我们为光滑类别给出了非退化左对称代数的分类，对于解析类则给出了一些小差距。解析和平滑这两种情况是不同的。我们还获得了二维实左对称代数的完整分类，