Geodesic
Quasi-local algebras and asymptotic expanders
Kang Li1 orcid ; Piotr W. Nowak1 orcid ; Ján Špakula2 ; Jiawen Zhang2 orcid
1Polish Academy of Sciences, Warsaw, Poland
2University of Southampton, UK
Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 655-682

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DOI

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.
DOI : 10.4171/ggd/610
Classification : 46-XX, 05-XX, 20-XX
Mots-clés : Expanders, Nuclearity, Property A, Quasi-local algebras

Kang Li  1   ; Piotr W. Nowak  1   ; Ján Špakula  2   ; Jiawen Zhang  2

1 Polish Academy of Sciences, Warsaw, Poland
2 University of Southampton, UK 
Kang Li; Piotr W. Nowak; Ján Špakula; Jiawen Zhang. Quasi-local algebras and asymptotic expanders. Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 655-682. doi: 10.4171/ggd/610
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     title = {Quasi-local algebras and asymptotic expanders},
     journal = {Groups, geometry, and dynamics},
     pages = {655--682},
     year = {2021},
     volume = {15},
     number = {2},
     doi = {10.4171/ggd/610},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/610/}
}
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