Embedding universality for II$_1$ factors with property (T)
Operator Algebras
2022-05-17 v1 Dynamical Systems
Group Theory
Abstract
We prove that every separable tracial von Neumann algebra embeds into a II factor with property (T) which can be taken to have trivial outer automorphism and fundamental groups. We also establish an analogous result for the trivial extension over a non-atomic probability space of every countable p.m.p. equivalence relation. These results are obtained by using the class of wreath-like product groups introduced recently in \cite{CIOS21}.
Keywords
Cite
@article{arxiv.2205.07442,
title = {Embedding universality for II$_1$ factors with property (T)},
author = {Ionut Chifan and Daniel Drimbe and Adrian Ioana},
journal= {arXiv preprint arXiv:2205.07442},
year = {2022}
}