### Abstract

We prove that there are examples of finitely generated groups Γ together with group ring elements Q∈QΓ for which the von Neumann dimension dim_{LΓ} ker Q is irrational, thus (in conjunction with other known results) answering a question of Atiyah.

Original language | English (US) |
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Pages (from-to) | 1424-1448 |

Number of pages | 25 |

Journal | Proceedings of the London Mathematical Society |

Volume | 107 |

Issue number | 6 |

DOIs | |

State | Published - Dec 2013 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the London Mathematical Society*,

*107*(6), 1424-1448. https://doi.org/10.1112/plms/pdt029

**Rational group ring elements with kernels having irrational dimension.** / Austin, Tim.

Research output: Contribution to journal › Article

*Proceedings of the London Mathematical Society*, vol. 107, no. 6, pp. 1424-1448. https://doi.org/10.1112/plms/pdt029

}

TY - JOUR

T1 - Rational group ring elements with kernels having irrational dimension

AU - Austin, Tim

PY - 2013/12

Y1 - 2013/12

N2 - We prove that there are examples of finitely generated groups Γ together with group ring elements Q∈QΓ for which the von Neumann dimension dimLΓ ker Q is irrational, thus (in conjunction with other known results) answering a question of Atiyah.

AB - We prove that there are examples of finitely generated groups Γ together with group ring elements Q∈QΓ for which the von Neumann dimension dimLΓ ker Q is irrational, thus (in conjunction with other known results) answering a question of Atiyah.

UR - http://www.scopus.com/inward/record.url?scp=84890584572&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84890584572&partnerID=8YFLogxK

U2 - 10.1112/plms/pdt029

DO - 10.1112/plms/pdt029

M3 - Article

VL - 107

SP - 1424

EP - 1448

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 6

ER -