Lehmer's Problem for arbitrary groups
Operator Algebras
2020-09-18 v2 Number Theory
Abstract
We consider the problem whether for a group G there exists a constant Lambda(G) > 1 such that for any (r,s)-matrix A over the integral group ring ZG the Fuglede-Kadison determinant of the G-equivariant bounded operator from L^2(G)^r to L^2(G)^s given by right multiplication with A is either one or greater or equal to Lambda(G). If G is the infinite cyclic group and we consider only r = s = 1, this is precisely Lehmer's problem.
Cite
@article{arxiv.1901.00827,
title = {Lehmer's Problem for arbitrary groups},
author = {Wolfgang Lueck},
journal= {arXiv preprint arXiv:1901.00827},
year = {2020}
}
Comments
25 pages, final version, to appear in Journal of Topology and Analysis