The rank of finitely generated modules over group algebras
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- by Gábor Elek
- Proc. Amer. Math. Soc. 131 (2003), 3477-3485
- DOI: https://doi.org/10.1090/S0002-9939-03-06908-9
- Published electronically: February 6, 2003
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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
Bibliographic 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