2,919 research outputs found
Rational group ring elements with kernels having irrational dimension
We prove that there are examples of finitely generated groups G together with
group ring elements Q \in \bbQ G for which the von Neumann dimension
\dim_{LG}\ker Q is irrational, so (in conjunction with other known results)
answering a question of Atiyah.Comment: 35 pages, 1 figure; [TDA 3/12/13:] Updated version incorporating
referee's suggestion
Quantitative equidistribution for certain quadruples in quasi-random groups
In a recent paper (arXiv:1211.6372), Bergelson and Tao proved that if is
a -quasi-random group, and , are drawn uniformly and independently
from , then the quadruple is roughly equidistributed in the
subset of defined by the constraint that the last two coordinates lie in
the same conjugacy class. Their proof gives only a qualitative version of this
result. The present notes gives a rather more elementary proof which improves
this to an explicit polynomial bound in .Comment: 5 pages; [TDA Jun 6, 2014] Updated with reference to arxiv:1405.5629
[v3:] This preprint has been re-written to correct to a mistake in the proof
of Corollary 3. The journal published that correction in a separate erratu
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