There Is An Equivalence Relation Whose von Neumann Algebra Is Not Connes Embeddable
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914443864047616 |
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| author | Manzoor, Aareyan |
| author_facet | Manzoor, Aareyan |
| contents | The landmark quantum complexity result MIP$^*$=RE was used to prove the existence of a non Connes embeddable tracial von Neumann algebra. Recently, similar ideas were used to give a negative solution to the Aldous-Lyons conjecture: there is a non co-sofic IRS on any non-abelian free group. We define a notion of hyperlinearity for an IRS and show that there is a non co-hyperlinear IRS on any non-abelian free group. As a corollary, we prove that there is a relation whose von Neumann algebra is not Connes embeddable. We do this by significantly simplifying the reduction of Aldous-Lyons to non-local games, removing the need for subgroup tests entirely. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | There Is An Equivalence Relation Whose von Neumann Algebra Is Not Connes Embeddable Manzoor, Aareyan Operator Algebras Group Theory 46L99 The landmark quantum complexity result MIP$^*$=RE was used to prove the existence of a non Connes embeddable tracial von Neumann algebra. Recently, similar ideas were used to give a negative solution to the Aldous-Lyons conjecture: there is a non co-sofic IRS on any non-abelian free group. We define a notion of hyperlinearity for an IRS and show that there is a non co-hyperlinear IRS on any non-abelian free group. As a corollary, we prove that there is a relation whose von Neumann algebra is not Connes embeddable. We do this by significantly simplifying the reduction of Aldous-Lyons to non-local games, removing the need for subgroup tests entirely. |
| title | There Is An Equivalence Relation Whose von Neumann Algebra Is Not Connes Embeddable |
| topic | Operator Algebras Group Theory 46L99 |
| url | https://arxiv.org/abs/2502.06697 |