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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The rank of finitely generated modules over group algebras
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by Gábor Elek PDF
Proc. Amer. Math. Soc. 131 (2003), 3477-3485 Request permission

Abstract:

We show the existence of a rank function on finitely generated modules over group algebras $K\Gamma$, where $K$ is an arbitrary field and $\Gamma$ is a finitely generated amenable group. This extends a result of W. Lück (1998).
References
  • G. Elek, Amenable groups, topological entropy and Betti numbers. (to appear in the Israel Journal of Mathematics)
  • Wolfgang Lück, Dimension theory of arbitrary modules over finite von Neumann algebras and $L^2$-Betti numbers. II. Applications to Grothendieck groups, $L^2$-Euler characteristics and Burnside groups, J. Reine Angew. Math. 496 (1998), 213–236. MR 1605818, DOI 10.1515/crll.1998.031
  • Donald S. Ornstein and Benjamin Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Analyse Math. 48 (1987), 1–141. MR 910005, DOI 10.1007/BF02790325
  • David Ruelle, Thermodynamic formalism, Encyclopedia of Mathematics and its Applications, vol. 5, Addison-Wesley Publishing Co., Reading, Mass., 1978. The mathematical structures of classical equilibrium statistical mechanics; With a foreword by Giovanni Gallavotti and Gian-Carlo Rota. MR 511655
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Additional Information
  • Gábor Elek
  • Affiliation: Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary
  • MR Author ID: 360750
  • Email: elek@renyi.hu
  • Received by editor(s): November 14, 2001
  • Received by editor(s) in revised form: May 31, 2002
  • Published electronically: February 6, 2003
  • Communicated by: Martin Lorenz
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 3477-3485
  • MSC (2000): Primary 43A07, 20C07
  • DOI: https://doi.org/10.1090/S0002-9939-03-06908-9
  • MathSciNet review: 1991759