Rational group ring elements with kernels having irrational dimension
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.
 Publication:

arXiv eprints
 Pub Date:
 September 2009
 arXiv:
 arXiv:0909.2360
 Bibcode:
 2009arXiv0909.2360A
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Dynamical Systems;
 Mathematics  Geometric Topology;
 Mathematics  Operator Algebras;
 20F65 (Primary);
 58J22;
 05C25 (Secondary)
 EPrint:
 35 pages, 1 figure