任意一致局部有限粗空间上一致 Roe 代数的同构刚性
Isomorphism rigidity of uniform Roe algebras over arbitrary uniformly locally finite coarse spaces
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中文总结 AI 辅助
研究任意一致局部有限粗空间上一致 Roe 代数的同构刚性问题，通过证明\(C^*\) - 代数同构能推出空间双射粗等价，解决了该同构刚性问题。
中文摘要 AI 辅助
设\((X,\mathcal E)\)和\((Y,\mathcal F)\)为一致局部有限粗空间。我们证明，每个\(C^*\) - 代数同构\(C_u^*(X,\mathcal E)\cong C_u^*(Y,\mathcal F)\)都迫使\((X,\mathcal E)\)和\((Y,\mathcal F)\)是双射粗等价的。这完全解决了任意一致局部有限粗空间上一致 Roe 代数的同构刚性问题。
英文摘要
Let $(X,\mathcal E)$ and $(Y,\mathcal F)$ be uniformly locally finite coarse spaces. We prove that every $C^*$-algebra isomorphism $C_u^*(X,\mathcal E)\cong C_u^*(Y,\mathcal F)$ forces $(X,\mathcal E)$ and $(Y,\mathcal F)$ to be bijectively coarsely equivalent. This completely resolves the isomorphism rigidity problem for uniform Roe algebras over arbitrary uniformly locally finite coarse spaces.
