论文标题
二维持续部分的对称性
Symmetries of a two-dimensional continued fraction
论文作者
论文摘要
在本文中，我们描述了二维持续部分的对称性组。作为持续分数的多维概括，我们认为klein polyhedra。我们区分了两种类型的对称性：dirichlet-type型，它们对应于相应数字字段的单位的乘法，而所谓的palindromic则对应。本文的主要结果是二维持续分数的标准，其具有对称性的对称性。该标准类似于二次非理性时期的标准。
In this paper we describe the group of symmetries of a two-dimensional continued fraction. As a multidimensional generalization of continued fractions we consider Klein polyhedra. We distinguish two types of symmetries: the Dirichlet-type ones, that correspond to the multiplication by units of the corresponding number field, and so called palindromic ones. The main result of the paper is a criterion for a two-dimensional continued fraction to have a palindromic symmetry. This criterion is analogous to the criterion for the period of a quadratic irrationality to be symmetric.
