All generating sets of all property T von Neumann algebras have free entropy dimension $\leq 1$
| dc.creator | Jung, Kenley | |
| dc.creator | Shlyakhtenko, Dimitri | |
| dc.date | 2006-03-28 | |
| dc.date | 2006-03-29 | |
| dc.date.accessioned | 2026-07-07T07:07:18Z | |
| dc.date.available | 2026-07-07T07:07:18Z | |
| dc.description | Suppose $N$ is a diffuse, property T von Neumann algebra and X is an arbitrary finite generating set of selfadjoint elements for N. By using rigidity/deformation arguments applied to representations of N in full matrix algebras, we deduce that the microstate spaces of X are asymptotically discrete up to unitary conjugacy. We use this description to show that the free entropy dimension of X, $δ_0(X)$, is less than or equal to 1. It follows that when N embeds into the ultraproduct of the hyperfinite $\mathrm{II}_1$-factor, then $δ_0(X)=1$ and otherwise, $δ_0(X)=-\infinity$. This generalizes the earlier results of Voiculescu, and Ge, Shen pertaining to $SL_n(\mathbb Z)$ as well as the results of Connes, Shlyakhtenko pertaining to group generators of arbitrary property T algebras. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603669 | |
| dc.identifier | http://arxiv.org/abs/math/0603669 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110345 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L54; 52C17 | |
| dc.title | All generating sets of all property T von Neumann algebras have free entropy dimension $\leq 1$ | |
| dc.type | text |