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The rank of finitely generated modules over group algebras
Author:
Gábor Elek
Journal:
Proc. Amer. Math. Soc. 131 (2003), 3477-3485
MSC (2000):
Primary 43A07, 20C07
Posted:
February 6, 2003
MathSciNet review:
1991759
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Abstract: We show the existence of a rank function on finitely generated modules over group algebras  , where  is an arbitrary field and  is a finitely generated amenable group. This extends a result of W. Lück (1998).
- 1.
G. ELEK, Amenable groups, topological entropy and Betti numbers. (to appear in the Israel Journal of Mathematics)
- 2.
Wolfgang
Lück, Dimension theory of arbitrary modules over finite von
Neumann algebras and 𝐿²-Betti numbers. II. Applications to
Grothendieck groups, 𝐿²-Euler characteristics and Burnside
groups, J. Reine Angew. Math. 496 (1998),
213–236. MR 1605818
(99k:58177), http://dx.doi.org/10.1515/crll.1998.031
- 3.
Donald
S. Ornstein and Benjamin
Weiss, Entropy and isomorphism theorems for actions of amenable
groups, J. Analyse Math. 48 (1987), 1–141. MR 910005
(88j:28014), http://dx.doi.org/10.1007/BF02790325
- 4.
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
(80g:82017)
- 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
 -Betti numbers. II: Applications to Grothendieck groups,  -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:
http://dx.doi.org/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
Article copyright:
© Copyright 2003 American Mathematical Society
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