Unitary representations and von Neumann's continuous geometries
Group Theory
2026-04-30 v1 Operator Algebras
Rings and Algebras
Representation Theory
Abstract
We prove that the unit group of a non-discrete irreducible, continuous ring, in the sense of John von Neumann, does not admit any non-trivial unitary representation continuous with respect to the strong operator topology.
Cite
@article{arxiv.2604.26104,
title = {Unitary representations and von Neumann's continuous geometries},
author = {Friedrich Martin Schneider and Andreas Thom},
journal= {arXiv preprint arXiv:2604.26104},
year = {2026}
}
Comments
15 pages, no figures