论文标题
I型局部紧凑量量子组的共同性
Coamenability of type I locally compact quantum groups
论文作者
论文摘要
我们建立了与I型局部紧凑型量子组相当的两个条件。第一个条件与空间上某些卷积运算符的光谱有关$ \ operatorName {l}^2（\ propatoTorname {irraTorname {ilr}（\ mathbb {g}）$，这些函数是与plancherel度量相对于平方集成的函数。第二条件涉及与不可还能表示的直接积分相关的字符样算子的光谱。作为示例，我们研究了量子组的特殊类别：经典，经典，紧凑或由某些双层产品结构给出。
We establish two conditions equivalent to coamenability for type I locally compact quantum groups. The first condition is concerned with the spectra of certain convolution operators on the space $\operatorname{L}^2(\operatorname{Irr}(\mathbb{G}))$ of functions which are square integrable with respect to the Plancherel measure. The second condition involves spectra of character-like operators associated with direct integrals of irreducible representations. As examples we study special classes of quantum groups: classical, dual to classical, compact or given by a certain bicrossed product construction.
