Elementary equivalence and disintegration of tracial von Neumann algebras
D Gao, D Jekel - arXiv preprint arXiv:2410.05529, 2024 - arxiv.org
We prove an analog of the disintegration theorem for tracial von Neumann algebras in the
setting of elementary equivalence rather than isomorphism, showing that elementary …
setting of elementary equivalence rather than isomorphism, showing that elementary …
Upgraded free independence phenomena for random unitaries
D Jekel, SK Elayavalli - arXiv preprint arXiv:2404.17114, 2024 - arxiv.org
We study upgraded free independence phenomena for unitary elements $ u_1 $, $ u_2
$,\dots in a matrix ultraproduct constructed from the large-$ n $ limit of Haar random …
$,\dots in a matrix ultraproduct constructed from the large-$ n $ limit of Haar random …
Internal sequential commutation and single generation
D Gao, SK Elayavalli, G Patchell, H Tan - arXiv preprint arXiv:2404.12380, 2024 - arxiv.org
We extract a precise internal description of the sequential commutation equivalence relation
introduced in [KEP23] for tracial von Neumann algebras. As an application we prove that if a …
introduced in [KEP23] for tracial von Neumann algebras. As an application we prove that if a …
Back-and-forth equivalent group von Neumann algebras
I Goldbring, M Harrison-Trainor - arXiv preprint arXiv:2403.16181, 2024 - arxiv.org
We prove that if $ G $ and $ H $ are $\alpha $-back-and-forth equivalent groups (in the
sense of computable structure theory) for some ordinal $\alpha\geq\omega $, then their …
sense of computable structure theory) for some ordinal $\alpha\geq\omega $, then their …
Simplices of maximally amenable extensions in II factors
SK Elayavalli, G Patchell - arXiv preprint arXiv:2410.11788, 2024 - arxiv.org
For every $ n\in\mathbb {N} $ we obtain a separable II $ _1 $ factor $ M $ and a maximally
abelian subalgebra $ A\subset M $ such that the space of maximally amenable extensions …
abelian subalgebra $ A\subset M $ such that the space of maximally amenable extensions …
On conjugacy and perturbation of subalgebras
D Gao, SK Elayavalli, G Patchell, H Tan - arXiv preprint arXiv:2403.08072, 2024 - arxiv.org
We study conjugacy orbits of certain types of subalgebras in tracial von Neumann algebras.
For any separable II $ _1 $ factor $ N_0 $ we construct a highly indecomposable non …
For any separable II $ _1 $ factor $ N_0 $ we construct a highly indecomposable non …