Quasi-local algebras and asymptotic expanders
Li K, Nowak P, Spakula J, Zhang J (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 15
Pages Range: 655-682
Journal Issue: 2
DOI: 10.4171/GGD/610
Abstract
In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic expanders. We show that being a sequence of asymptotic expanders is a coarse property under certain connectedness condition, and it implies non-uniformly local amenability. Moreover, we also analyse some C *-algebraic properties of uniform quasi-local algebras. In particular, we show that a uniform quasi-local algebra is nuclear if and only if the underlying metric space has Property A.
Authors with CRIS profile
Involved external institutions
Polska Akademia Nauk (PAN) / Polish Academy of Sciences
Poland (PL)
University of Southampton
United Kingdom (GB)
Mathematical Institute of the Polish Academy of Sciences
Poland (PL)
Poland (PL)
University of Southampton
United Kingdom (GB)
Mathematical Institute of the Polish Academy of Sciences
Poland (PL)
How to cite
APA:
Li, K., Nowak, P., Spakula, J., & Zhang, J. (2021). Quasi-local algebras and asymptotic expanders. Groups Geometry and Dynamics, 15(2), 655-682. https://dx.doi.org/10.4171/GGD/610
MLA:
Li, Kang, et al. "Quasi-local algebras and asymptotic expanders." Groups Geometry and Dynamics 15.2 (2021): 655-682.
BibTeX: Download