Uniform Roe algebras of uniformly locally finite metric spaces are rigid
Uniform Roe algebras of uniformly locally finite metric spaces are rigid
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DOI：
10.1007/s00222-022-01140-x
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发表时间：
2021-06
影响因子：
3.1
通讯作者：
F. Baudier;B. M. Braga;I. Farah;A. Khukhro;A. Vignati;R. Willett
中科院分区：
文献类型：
--
作者：
F. Baudier;B. M. Braga;I. Farah;A. Khukhro;A. Vignati;R. Willett
我们证明，如果 X 和 Y 是一致局部有限度量空间，其一致 Roe 代数 和 是同构代数，则 X 和 Y 是粗略等价度量空间。此外，我们证明X和Y之间的粗略等价相当于和之间的Morita等价。作为一个应用，我们得到如果anda是有限生成群，那么交叉积and是同构的当且仅当anda是bi-Lipschitz等价的。
We show that ifXandYare uniformly locally finite metric spaces whose uniform Roe algebras,and, are isomorphic as-algebras, thenXandYare coarsely equivalent metric spaces. Moreover, we show that coarse equivalence betweenXandYis equivalent to Morita equivalence betweenand. As an application, we obtain that ifandare finitely generated groups, then the crossed productsandare isomorphic if and only ifandare bi-Lipschitz equivalent.