Rational group ring elements with kernels having irrational dimension

2009/09/30 by Tim Austin · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Finite Group Theory Research #Geometric and Algebraic Topology #math.DS #math.GR #math.GT #math.OA #msc:05C25 #msc:20F65 #msc:58J22

paper · pdf · doi:10.1112/plms/pdt029

35 pages, 1 figure; [TDA 3/12/13:] Updated version incorporating referee's suggestions

arxiv created 2013/03/12 · openalex publication_date 2013/07/09 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 dimLΓ ker Q is irrational, thus (in conjunction with other known results) answering a question of Atiyah.

Citations

• Modern Graph Theory
• Approximating L2-invariants, and the Atiyah conjecture

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