论文标题
有限能量路径和循环组的不良性属性
An amenability-like property of finite energy path and loop groups
论文作者
论文摘要
我们表明，有限的能量回路和路径（即Sobolev类$ h^1 $）具有一个紧凑的连接谎言组的值以及它们的中心扩展，可以满足左右函数的左右均值均匀的平均值，而左右函数则符合左右的左右，而左右又有左右的属性。此类组的每个强烈连续的统一表示$π$（我们称为偏斜）在$ b（{\ Mathcal h}_π）上都具有连接不变的状态。
We show that the groups of finite energy loops and paths (that is, those of Sobolev class $H^1$) with values in a compact connected Lie group, as well as their central extensions, satisfy an amenability-like property: they admit a left-invariant mean on the space of bounded functions uniformly continuous with regard to a left-invariant metric. Every strongly continuous unitary representation $π$ of such a group (which we call skew-amenable) has a conjugation-invariant state on $B({\mathcal H}_π)$.
