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The rank of finitely generated modules over group algebras

Author(s): Gábor Elek
Journal: Proc. Amer. Math. Soc. 131 (2003), 3477-3485.
MSC (2000): Primary 43A07, 20C07
Posted: 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:

1.
G. ELEK, Amenable groups, topological entropy and Betti numbers. (to appear in the Israel Journal of Mathematics)

2.
W. L¨UCK, 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 99k:58177

3.
D. S. ORNSTEIN and B. WEISS, Entropy and isomorphism theorems for actions of amenable groups, J. Anal. Math 48 (1987) 1-141. MR 88j:28014

4.
D. RUELLE, Thermodynamic formalism, Encyclopedia of Mathematics and Its Applications, Addison-Wesley 5 (1978) MR 80g:82017

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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
Email: elek@renyi.hu

DOI: 10.1090/S0002-9939-03-06908-9
PII: S 0002-9939(03)06908-9
Keywords: Amenable groups, group algebras, finitely generated modules, invariant subspaces
Received by editor(s): November 14, 2001
Received by editor(s) in revised form: May 31, 2002
Posted: February 6, 2003
Communicated by: Martin Lorenz
Copyright of article: Copyright 2003, American Mathematical Society

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