Journal of Operator Theory
Volume 80, Issue 1, Summer 2018 pp. 25-46.
Classification of uniform Roe algebras of locally finite groups
Authors:
Kang Li (1) and Hung-Chang Liao (2)
Author institution: (1) Mathematisches Institut der WWU Munster, Munster, 48149,
Deutschland
(2) Mathematisches Institut der WWU Munster, Munster, 48149, Deutschland
Summary: We show that for two countable locally finite groups Γ and
Λ, the associated uniform Roe algebras C∗u(Γ) and
C∗u(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)⋊ is locally
finite-dimensional.
DOI: http://dx.doi.org/10.7900/jot.2017may23.2163
Keywords: uniform Roe algebras, classification of C^*-algebras, coarse geometry
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