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A class of II1 factors without non-trivial crossed product decompositions
Abstract
We introduce a class of separable II1 factors M admitting no non-trivial crossed product decompositions: Mnot≅ BrtimesσG, for any trace preserving action Gcurvearrowrightσ(B,τ) of an infinite countable group G on a tracial von Neumann algebra (B,τ). These provide the first examples of II1 factors that do not arise as crossed products of noncommutative dynamical systems. Our approach relies on a novel construction of separable II1 factors M whose embeddings into their tensor product square M⊗̅M all arise from the canonical embeddings x↦ x⊗ 1 and x↦ 1⊗ x.
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BibTeX
@misc{quero2026class,
title = {{A class of II$_1$ factors without non-trivial crossed product decompositions}},
author = {Adriana Fernández Quero and Adrian Ioana and Hui Tan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.31929},
eprint = {2606.31929},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.31929},
}
RIS
TY - UNPB
TI - A class of II_1 factors without non-trivial crossed product decompositions
AU - Adriana Fernández Quero
AU - Adrian Ioana
AU - Hui Tan
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2606.31929
UR - https://arxiv.org/abs/2606.31929
AB - We introduce a class of separable II_1 factors M admitting no non-trivial crossed product decompositions: Mnot≅ Brtimes_σG, for any trace preserving action Gcurvearrowright^σ(B,τ) of an infinite countable group G on a tracial von Neumann algebra (B,τ). These provide the first examples of II_1 factors that do not arise as crossed products of noncommutative dynamical systems. Our approach relies on a novel construction of separable II_1 factors M whose embeddings into their tensor product square M⊗̅M all arise from the canonical embeddings x↦ x⊗ 1 and x↦ 1⊗ x.
ER -