Lehmer's Problem for arbitrary groups

Wolfgang Lueck

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arXiv · 1901.00827

Lehmer's Problem for arbitrary groups

Wolfgang Lueck

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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.

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BibTeX RIS

Wolfgang Lueck. 2019-01-03. Lehmer's Problem for arbitrary groups. https://arxiv.org/abs/1901.00827

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