The von Neumann algebra of the non-residually finite Baumslag group < a,b | a b^3 a^-1 = b^2 > embeds into R^omega
| dc.creator | Radulescu, Florin | |
| dc.date | 2000-04-27 | |
| dc.date | 2002-02-13 | |
| dc.date.accessioned | 2026-07-07T04:34:54Z | |
| dc.date.available | 2026-07-07T04:34:54Z | |
| dc.description | In this paper we analyze the structure of some sets of non-commutative moments of elements in a finite von Neumann algebra M. If the fundamental group of M is R_+\{0}, then the moment sets are convex, and if M is isomorphic to M tensor M, then the sets are closed under pointwise multiplication. We introduce a class of discrete groups that we call hyperlinear. These are the discrete subgroups (with infinite conjugacy classes) of the unitary group of R^omega. We prove that this class is strictly larger than the class of (i.c.c.) residually finite groups. In particular, it contains the Baumslag group < a,b | a b^3 a^-1 = b^2 >. This leads to a previously unknown (non-hyperfinite) type II_1 factor that can be embedded in R^omega. This is positive evidence for Connes's conjecture that any separable II_1 factor can be embedded into R^omega. | |
| dc.description | LaTeX2e "amsart" class, 16 pages. Changes: (v2) small typos corrected and picture added; (v3) more descriptive title (formerly "Convex sets associated to von Neumann algebras II"); extensive corrections and clarifications particularly in Section 2 "Moments of Unitaries"; abstract edited, TeX sequences used to get around arXiv's treatment of angle brackets | |
| dc.identifier | https://arxiv.org/abs/math/0004172 | |
| dc.identifier | http://arxiv.org/abs/math/0004172 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59084 | |
| dc.subject | Operator Algebras | |
| dc.title | The von Neumann algebra of the non-residually finite Baumslag group < a,b | a b^3 a^-1 = b^2 > embeds into R^omega | |
| dc.type | text |