We describe the symmetry group of a multidimensional continued fraction. As a multidimensional generalization of continued fractions we consider Klein polyhedra. We distinguish two types of symmetries: Dirichlet symmetries, which correspond to the multiplication by units of the respective extension of , and so-called palindromic symmetries. The main result is a criterion for a two-dimensional continued fraction to have palindromic symmetries, which is analogous to the well-known criterion for the continued fraction of a quadratic irrationality to have a symmetric period.

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二维连分数的对称性

我们描述了多维连分数的对称群。作为连分数的多维推广，我们考虑克莱因多面体。我们区分两种类型的对称性：Dirichlet 对称性，对应于 的相应扩展的单位的乘法，以及所谓的回文对称性。主要结果是二维连分数具有回文对称性的标准，类似于众所周知的二次无理连分数具有对称周期的标准。