Shranjeno v:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Izdano: |
2024
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| Teme: | |
| Online dostop: | https://arxiv.org/abs/2403.08072 |
| Oznake: |
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Kazalo:
- 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 Gamma II$_1$ factor $N$ such that $N_0 \subset N$ and moreover every von Neumann subalgebra of $N$ with Haagerup's property admits a unique embedding up to unitary conjugation. Such a factor necessarily has to be non separable, but we show that it can be taken of density character $2^{\aleph_0}$. On the other hand we are able to construct for any separable II$_1$ factor $M_0$, a separable II$_1$ factor $M$ containing $M_0$ such that every property (T) subfactor admits a unique embedding into $M$ up to uniformly approximate unitary equivalence; i.e., any pair of embeddings can be conjugated up to a small uniform $2$-norm perturbation.