The $K$-theory of Gromov’s translation algebras and the amenability of discrete groups
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- by Gábor Elek PDF
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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.References
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Additional Information
- Gábor Elek
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
- Address at time of publication: Mathematical Institute, Hungarian Academy of Science, P. O. Box 127, H-1364 Budapest, Hungary
- MR Author ID: 360750
- Email: elekgab@math.purdue.edu, elek@math-inst.hu
- Received by editor(s): April 9, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2551-2553
- MSC (1991): Primary 20F38
- DOI: https://doi.org/10.1090/S0002-9939-97-04056-2
- MathSciNet review: 1415585