AI 中文总结
该研究证明无限标准概率空间上遍历变换的自同构群及其反向自同构群可实现为图的对称群，回答了Lovasz的问题并构造了具高度可变对称性的图族。
AI 中文摘要
我们证明，对于无限标准概率空间上的每个遍历变换$T$，其自同构群（即中心化子）$\text{Aut}(T)$及其反向自同构群均可实现为图的对称群。这是Sabidussi关于任意图自同构群实现的类比，提供了大量无相容紧拓扑的图自同构群实例，回答了Lovasz的问题。相关讨论及后续构造的另一结论是存在具有高度可变对称性的大的相互局部-全局等价图族。
英文摘要
We prove that for every ergodic transformation $T$ on an infinite standard probability space both the automorphism group (i.e. centralizer) $\mathrm{Aut}(T)$ and its reversing automorphism group are realizable as symmetry groups of graphings. This is an analogue of Sabidussi's realization of arbitrary graph-automorphism groups, and provides numerous examples of graphing automorphism groups carrying no compatible compact topology, answering a question of Lovasz'. Another consequence of discussion and ensuing constructions is the existence of large mutually locally-globally equivalent graphing families with highly variable symmetry.
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