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Connes-embeddability and twisted group von Neumann algebras
Abstract
We call a countable discrete group cocycle-hyperlinear if all its twisted group von Neumann algebras are Connes-embeddable. We show that the class of cocycle-hyperlinear groups includes extensions of treeable groups by amenable groups and central extensions of SL(n,Z), GL(n,Z) and PSL(n,Z) for n greater than 1. We also show that this class is closed under taking direct products, free products, amalgamated free products with amenable amalgams, HNN extensions by amenable groups, as well as certain quotients, extensions, and overgroups.
Related
- Von Neumann algebras as reduced twisted groupoid C*-algebras
- Associativity of operator convolutions for group actions on von Neumann algebras
- Group actions on von Neumann algebras with compact open subgroups
- IRA Rigidity and boomerang subalgebras of group von Neumann algebras
- Selflessness for twisted group C*-algebras of amenable groups and their inclusions
BibTeX
@misc{chakraborty2026connesembeddability,
title = {{Connes-embeddability and twisted group von Neumann algebras}},
author = {Soham Chakraborty and Felipe Flores},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40246},
eprint = {2609.40246},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40246},
}
RIS
TY - UNPB
TI - Connes-embeddability and twisted group von Neumann algebras
AU - Soham Chakraborty
AU - Felipe Flores
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40246
UR - https://arxiv.org/abs/2609.40246
AB - We call a countable discrete group cocycle-hyperlinear if all its twisted group von Neumann algebras are Connes-embeddable. We show that the class of cocycle-hyperlinear groups includes extensions of treeable groups by amenable groups and central extensions of SL(n,Z), GL(n,Z) and PSL(n,Z) for n greater than 1. We also show that this class is closed under taking direct products, free products, amalgamated free products with amenable amalgams, HNN extensions by amenable groups, as well as certain quotients, extensions, and overgroups.
ER -