Remote Access Proceedings of the American Mathematical Society
Green Open Access

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

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. J. Block, S. Weinberger, Aperiodic tilings, positive scalar curvature and amenability of spaces, Journal of the Amer. Math. Soc. 5 (1992), 907-918 MR 93d:53054
  • 2. W.A.Deuber,M.Simonovits and V.T.Sós, A note on paradoxical metric spaces, Studia Sci.Hung.Math. 30 (1995), 17-23 MR 96i:54025
  • 3. M.Gromov, Asymptotic Invariants of Infinite Groups, London Math. Society, Lecture Note Series 182 (1993) MR 95m:20041
  • 4. J. Roe, An index theorem on open manifolds I-II, Journal of Differential Geometry 27 (1988), 87-136 MR 89a:58102
  • 5. P.M.Soardi, Potential Theory on Infinite Networks, Lecture Notes in Mathematics 1590 MR 96i:31005

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20F38

Retrieve articles in all journals with MSC (1991): 20F38


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
Email: elekgab@math.purdue.edu, elek@math-inst.hu

DOI: https://doi.org/10.1090/S0002-9939-97-04056-2
Received by editor(s): April 9, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society