PreprintCC BY 4.0arXiv
Lifting for N-independent sets in II1 factors
Abstract
In a tracial von Neumann algebra M, two subsets X and Y are said to be N-independent if alternating products of length at most N of trace zero words from X and Y have trace zero. We show that two approximately 2N-independent finite tuples can be perturbed, in operator norm, to be exactly N-independent. Consequently, we are able to generalize Theorem 5.1 and Theorem H of Houdayer-Ioana and resolve Problem 31 of Kunnawalkam Elayavalli in the positive.
Related
BibTeX
@misc{patchell2026lifting,
title = {{Lifting for N-independent sets in II1 factors}},
author = {Gregory Patchell and Austin Shiner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10087},
eprint = {2609.10087},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10087},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lifting for N-independent sets in II1 factors
AU - Gregory Patchell
AU - Austin Shiner
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10087
UR - https://arxiv.org/abs/2609.10087
AB - In a tracial von Neumann algebra M, two subsets X and Y are said to be N-independent if alternating products of length at most N of trace zero words from X and Y have trace zero. We show that two approximately 2N-independent finite tuples can be perturbed, in operator norm, to be exactly N-independent. Consequently, we are able to generalize Theorem 5.1 and Theorem H of Houdayer-Ioana and resolve Problem 31 of Kunnawalkam Elayavalli in the positive.
ER -