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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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

Author: Gábor Elek
Journal: Proc. Amer. Math. Soc. 125 (1997), 2551-2553
MSC (1991): Primary 20F38
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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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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

PII: S 0002-9939(97)04056-2
Received by editor(s): April 9, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society