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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

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

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