The centralizer (automorphism group) and normalizer (extended symmetry group) of the shift action inside the group of self-homeomorphisms are studied, in the context of certain $ \mathbb{Z}^d $ subshifts with a hierarchical supertile structure, such as bijective substitutive subshifts and the Robinson tiling. Restrictions on these groups via geometrical considerations are used to characterize explicitly their structure: nontrivial extended symmetries can always be described via relabeling maps and rigid transformations of the Euclidean plane permuting the coordinate axes. The techniques used also carry over to the well-known Robinson tiling, both in its minimal and non-minimal versions.

中文翻译：

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具有层次结构的多维子移位的扩展对称组

在具有同级超小结构的某些$ \ mathbb {Z} ^ d $子移位的情况下，研究了自同态组内部移位动作的扶正器（自同构组）和归一化器（扩展对称组）。双宾语替换性子移位和Robinson平铺。出于几何考虑，对这些组的限制用于明确表征其结构：总是可以通过重新标注图和置换坐标轴的欧几里得平面的刚性变换来描述非平凡的扩展对称性。所使用的技术也以其最小版本和非最小版本延续到著名的Robinson平铺。