Rational group ring elements with kernels having irrational dimension
Group Theory
2014-02-26 v3 Dynamical Systems
Geometric Topology
Operator Algebras
Abstract
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.
Cite
@article{arxiv.0909.2360,
title = {Rational group ring elements with kernels having irrational dimension},
author = {Tim Austin},
journal= {arXiv preprint arXiv:0909.2360},
year = {2014}
}
Comments
35 pages, 1 figure; [TDA 3/12/13:] Updated version incorporating referee's suggestions