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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