On automorphism groups of Toeplitz subshifts
On automorphism groups of Toeplitz subshifts
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关于托普利茨子移的自同构群
DOI：
10.19086/da.1832
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
S. Petite
中科院分区：
文献类型：
--
作者：
S. Donoso;F. Durand;A. Maass;S. Petite
本文研究Toeplitz子移位的自同构。这样的群是交换的，并且任何有限生成的扭子群都是有限的循环的。当复杂性为非超线性时，我们证明了自同构群是模有限循环群，由移位的唯一根生成。在次二次复杂性情形下，我们证明了模扭转的自同构群是由移位映射的根生成的，并且非线性超线性情形的结果是最优的。也就是说，对于任何$\varepsilon>；0$，我们构造了复杂性为$Cn^{1+e}$的最小Toeplitz子移位的例子，其自同构群不是有限生成的。最后，我们观察到合并和自同构群对复杂性没有限制，因为我们提供了一族合并的Toeplitz子移位，使得它们的自同构群是任意有限生成的具有循环扭子群的无限阿贝尔群(最终限制为移位的幂)。
In this article we study automorphisms of Toeplitz subshifts. Such groups are abelian and any finitely generated torsion subgroup is finite and cyclic. When the complexity is non superlinear, we prove that the automorphism group is, modulo a finite cyclic group, generated by a unique root of the shift. In the subquadratic complexity case, we show that the automorphism group modulo the torsion is generated by the roots of the shift map and that the result of the non superlinear case is optimal. Namely, for any $\varepsilon > 0$ we construct examples of minimal Toeplitz subshifts with complexity bounded by $C n^{1+e}$ whose automorphism groups are not finitely generated. Finally, we observe the coalescence and the automorphism group give no restriction on the complexity since we provide a family of coalescent Toeplitz subshifts with positive entropy such that their automorphism groups are arbitrary finitely generated infinite abelian groups with cyclic torsion subgroup (eventually restricted to powers of the shift).
影响因子：
1.3
作者：
Cyr, Van;Franks, John;Kra, Bryna
通讯作者：
Kra, Bryna