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The amenability and non-amenability of skew fields

Author(s): Gábor Elek
Journal: Proc. Amer. Math. Soc. 134 (2006), 637-644.
MSC (2000): Primary 12E15, 43A07
Posted: August 29, 2005
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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: 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
Posted: August 29, 2005
Communicated by: Martin Lorenz
Copyright of article: Copyright 2005, American Mathematical Society

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