AI 中文总结
本文定义余循环-超线性群，证明其包含特定扩张与中心扩张，并在多种群运算下封闭，从而推广 Connes-可嵌入性。
AI 中文摘要
我们称一个可数离散群为余循环-超线性群，如果其所有扭曲群 von Neumann 代数都是 Connes-可嵌入的。我们证明余循环-超线性群的类包含可树化群与顺从群的扩张，以及 n 大于 1 时 SL(n,Z)、GL(n,Z) 和 PSL(n,Z) 的中心扩张。我们还证明该类在取直积、自由积、带顺从融合的自由积、由顺从群进行的 HNN 扩张，以及某些商、扩张和超群运算下封闭。
英文摘要
We call a countable discrete group cocycle-hyperlinear if all its twisted group von Neumann algebras are Connes-embeddable. We show that the class of cocycle-hyperlinear groups includes extensions of treeable groups by amenable groups and central extensions of SL(n,Z), GL(n,Z) and PSL(n,Z) for n greater than 1. We also show that this class is closed under taking direct products, free products, amalgamated free products with amenable amalgams, HNN extensions by amenable groups, as well as certain quotients, extensions, and overgroups.
Commentsv1: 26 pages; comments welcome!
