arXiv math/00041722000-04math.OA

非剩余有限Baumslag群< a，b的von Neumann algebra| a b^3 a^-1 = b^2 >嵌入到R^omega中

The von Neumann algebra of the non-residually finite Baumslag group < a,b | a b^3 a^-1 = b^2 > embeds into R^omega

Florin Radulescu

备注：: 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

摘要：

本文分析了有限vonNeumann代数M中某些元素的非交换矩集的结构。若M的基本群是R +\{0}，则矩集是凸的;若M同构于M张量M，则矩集在点乘下是闭的.我们引入一类离散群，我们称之为超线性。这些是R^omega的酉群的离散子群（具有无限共轭类）。我们证明了这个类严格大于（i.c.c.）剩余有限群特别地，它包含Baumslag群< a，b| a b^3 a^-1 = b^2 >。这导致了一个先前未知的（非超有限的）II_1型因子，它可以嵌入R^omega。这是康纳斯猜想的积极证据，即任何可分离的II_1因子都可以嵌入R^omega。

英文摘要：

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.

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