Bounded Normal Generation and Invariant Automatic Continuity
Operator Algebras
2015-08-13 v2 Functional Analysis
Group Theory
Abstract
We study the question how quickly products of a fixed conjugacy class in the projective unitary group of a II-factor von Neumann algebra cover the entire group. Our result is that the number of factors that are needed is essentially as small as permitted by the -norm - in analogy to a result of Liebeck-Shalev for non-abelian finite simple groups. As an application of the techniques, we prove that every homomorphism from the projective unitary group of a II-factor to a polish SIN group is continuous. Moreover, we show that the projective unitary group of a II-factor carries a unique polish group topology.
Cite
@article{arxiv.1506.08549,
title = {Bounded Normal Generation and Invariant Automatic Continuity},
author = {Philip A. Dowerk and Andreas Thom},
journal= {arXiv preprint arXiv:1506.08549},
year = {2015}
}
Comments
v2 minor changes, 42 pages