Classification of uniform Roe algebras of locally finite groups

Li K, Liao HC (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Journal of Operator Theory Theta Foundation

Book Volume: 80

Pages Range: 25-46

Journal Issue: 1

DOI: 10.7900/jot.2017may23.2163

Abstract

We show that for two countable locally finite groups Γ and Λ, the associated uniform Roe algebras Cu*(Γ) and Cu* (Λ) are *-isomorphic if and only if their K0 groups are isomorphic as ordered abelian groups with units. Along the way we obtain a rigidity result: two countable locally finite groups are bijectively coarsely equivalent if and only if the associated uniform Roe algebras are *-isomorphic. We also show that a (not necessarily countable) discrete group Γ is locally finite if and only if the associated uniform Roe algebra ℓ∞(Γ) ⋊r Γ is locally finite-dimensional.

Authors with CRIS profile

Kang Li

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE)

How to cite

APA:

Li, K., & Liao, H.-C. (2018). Classification of uniform Roe algebras of locally finite groups. Journal of Operator Theory, 80(1), 25-46. https://dx.doi.org/10.7900/jot.2017may23.2163

MLA:

Li, Kang, and Hung-Chang Liao. "Classification of uniform Roe algebras of locally finite groups." Journal of Operator Theory 80.1 (2018): 25-46.

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