The 𝐾-theory of Gromov’s translation algebras and the amenability of discrete groups

Elek, Gábor

doi:10.1090/S0002-9939-97-04056-2

The $K$-theory of Gromov’s translation algebras and the amenability of discrete groups
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by Gábor Elek

Proc. Amer. Math. Soc. 125 (1997), 2551-2553

DOI: https://doi.org/10.1090/S0002-9939-97-04056-2

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Abstract:

We prove the following theorem. A finitely generated group $\Gamma$ is amenable if and only if $\boldsymbol {1}\neq \boldsymbol {0}$ in $K_0(T(\Gamma ))$, the algebraic $K$-theory group of its translation algebra.

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