# Embeddings of uniform Roe algebras

## TL;DR

This paper investigates how embeddings of uniform Roe algebras reflect large-scale geometric properties of metric spaces, aiming to understand stability under such algebraic embeddings.

## Contribution

It provides new insights into the relationship between metric space geometry and the algebraic structure of their uniform Roe algebras.

## Key findings

- Identifies conditions under which geometric properties are preserved
- Establishes criteria for embeddings of uniform Roe algebras
- Connects algebraic embeddings with large-scale geometry

## Abstract

In this paper, we study embeddings of uniform Roe algebras. Generally speaking, given metric spaces $X$ and $Y$, we are interested in which large scale geometric properties are stable under embedding of the uniform Roe algebra of $X$ into the uniform Roe algebra of $Y$.