# Rational group ring elements with kernels having irrational dimension

@article{Austin2013RationalGR,
title={Rational group ring elements with kernels having irrational dimension},
author={Tim Austin},
journal={Proceedings of The London Mathematical Society},
year={2013},
volume={107},
pages={1424-1448}
}
• Tim Austin
• Published 2013
• Mathematics
• Proceedings of The London Mathematical Society
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.

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