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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The amenability and non-amenability of skew fields


Author: Gábor Elek
Journal: Proc. Amer. Math. Soc. 134 (2006), 637-644
MSC (2000): Primary 12E15, 43A07
Published electronically: August 29, 2005
MathSciNet review: 2180879
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Abstract: We investigate the amenability of skew field extensions of the complex numbers. We prove that all skew fields of finite Gelfand-Kirillov transcendence degree are amenable. However there are both amenable and non-amenable finitely generated skew fields of infinite Gelfand-Kirillov transcendence degree.


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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/S0002-9939-05-08128-1
PII: S 0002-9939(05)08128-1
Keywords: Skew fields, amenable algebras, Gelfand-Kirillov transcendence degree, von Neumann algebras.
Received by editor(s): November 24, 2003
Received by editor(s) in revised form: June 15, 2004, and October 4, 2004
Published electronically: August 29, 2005
Communicated by: Martin Lorenz
Article copyright: © Copyright 2005 American Mathematical Society