数域中无幂整数及其移位空间的对称性
Symmetries of power-free integers in number fields and their shift spaces
AI总结：
本文研究了数域K整数环中保持k次无幂整数集合V_{K,k}的Z线性自同构群，证明其由域自同构与单位元乘法复合而成，并揭示了相关移位空间D_{K,k}的扩展对称群生成方式及系统间的拓扑非共轭性，最后将此概念推广至筛法。
摘要：
我们描述了数域K的整数环中保持k次无幂整数集合V_{K,k}的Z线性自同构群：每个这样的映射都是一个域自同构与一个单位元乘法的复合。我们证明这些映射连同平移生成了与V_{K,k}相关的移位空间D_{K,k}的扩展对称群。此外，我们证明没有两个这样的动力系统D_{K,k}和D_{L,l}是拓扑共轭的，且没有一个是另一个的因子系统。我们将k次无幂整数的概念推广到筛法，并研究了由此产生的容许移位空间。
英文摘要：
We describe the group of $\mathbb Z$-linear automorphisms of the ring of integers of a number field $K$ that preserve the set $V_{K,k}$ of $k$th power-free integers: every such map is the composition of a field automorphism and the multiplication by a unit. We show that those maps together with translations generate the extended symmetry group of the shift space $\mathbb D_{K,k}$ associated to $V_{K,k}$. Moreover, we show that no two such dynamical systems $\mathbb D_{K,k}$ and $\mathbb D_{L,l}$ are topologically conjugate and no one is a factor system of another. We generalize the concept of $k$th power-free integers to sieves and study the resulting admissible shift spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
