发表机构
LAMFA, Université de Picardie Jules Verne（亚眠大学皮卡第朱尔斯·凡尔纳大学 LAMFA 实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究剩余有限群下里程计及Toeplitz子移位的自同构与正规化子群，证明对$\mathbb{Z}^d$轨道等价正规化子可通约，对其他幂零群不成立，并构造低复杂度例子展示中心化子受限而正规化子可极大的灵活性。
AI 中文摘要
对于剩余有限群，我们研究了里程计及其符号扩展（即Toeplitz子移位）的自同构群和正规化子群。在与轨道等价理论的关联中，我们证明了当$G=\mathbb{Z}^d$时，两个连续轨道等价的$G$-里程计具有可通约的正规化子，但该结论对其他幂零群$G$不成立。任何Toeplitz子移位的自同构群和正规化子群都嵌入其底层里程计的自同构群和正规化子群；尽管存在这一约束，它们仍展现出相当大的灵活性。例如，我们构造了低复杂度的$G$-Toeplitz子移位的例子，其中心化子同构于$G$（或在另一极端，限制于其中心），但其正规化子群却尽可能大。
英文摘要
For residually finite groups, we study the automorphism and normalizer groups of odometers and their symbolic extensions: Toeplitz subshifts. In relation to orbit equivalence theory, we show that two continuous orbit equivalent $G$-odometers have commensurable normalizers when $G=\mathbb{Z}^d$, but that this result fails for other nilpotent groups $G$. The automorphism and normalizer groups of any Toeplitz subshift embed into those of its underlying odometer; despite this constraint, they exhibit considerable flexibility. For instance, we exhibit examples of low-complexity $G$-Toeplitz subshifts whose centralizer is isomorphic to $G$ (or, at the other extreme, restricted to its center) yet whose normalizer group is as large as possible.
Comments26 pages. Comments are welcome!
