On the rigidity of uniform Roe algebras over uniformly locally finite coarse spaces

2018/05/11 by Braga, Bruno de Mendonça, Farah, Ilijas
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1805.04236

Abstract

Given a coarse space (X,E), one can define a C^*-algebra C^*_u(X) called the uniform Roe algebra of (X,E). It has been proved by J. Špakula and R. Willett that if the uniform Roe algebras of two uniformly locally finite metric spaces with property A are isomorphic, then the metric spaces are coarsely equivalent to each other. In this paper, we look at the problem of generalizing this result for general coarse spaces and on weakening the hypothesis of the spaces having property A.

Related

• General uniform Roe algebra rigidity
• Isomorphism rigidity of uniform Roe algebras over arbitrary uniformly locally finite coarse spaces
• Ideal structures and rigidity of uniform Roe algebras
• A rigidity framework for Roe-like algebras
• On Rigidity of Roe algebras