English

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

R2 v1 2026-06-21T13:45:45.697Z