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Australasian Research Symposium on Lie Groups, Algebraic Groups, Quantum Groups, and Their Representations (LAQ'2001)
December 7-10, 2001
The University of Auckland
Auckland, New Zealand

Organizers
Rod Gover (University of Auckland), Vladimir Pestov (Victoria University of Wellington)

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A new criterion of amenability for discrete groups.
by
Todd Rangiwhetu
Victoria University of Wellington

A group is amenable if it admits no decomposition into n pieces in such a way that translates of m < n of them cover the entire group, and so do translates of the n-m remaining pieces. This concept has its origins in the famous Banach-Tarski paradox. Presently the concept of amenability is of great importance, and numerous equivalent definitions are known. In this talk we will propose a new definition, based on the geometry of the unit sphere in the spaces lp (G) and the phenomenon of concentration of measure.

Date received: October 22, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahw-10.