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arXiv · 2310.03677

Embeddings of matrix algebras into uniform Roe algebras and quasi-local algebras

Narutaka Ozawa
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Abstract

We answer the recent problem posed by Baudier, Braga, Farah, Vignati, and Willett that asks whether the $\ell_\infty$-direct sum of the matrix algebras embeds into the uniform Roe algebra or the quasi-local algebra of a uniformly locally finite metric space. The answers are no and yes, respectively. Hence the inclusion of the uniform Roe algebra into the quasi-local algebra can be proper.

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Narutaka Ozawa. 2023-10-05. Embeddings of matrix algebras into uniform Roe algebras and quasi-local algebras. https://arxiv.org/abs/2310.03677

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