Building on recent progress in constructing derivations on Fourier algebras, we provide the first examples of locally compact groups whose Fourier algebras support non-zero, alternating 2-cocycles; this is the first step in a larger project. Although such 2-cocycles can never be completely bounded, the operator space structure on the Fourier algebra plays a crucial role in our construction, as does the opposite operator space structure.

Our construction has two main technical ingredients: we observe that certain estimates from [12] yield derivations that are “co-completely bounded” as maps from various Fourier algebras to their duals; and we establish a twisted inclusion result for certain operator space tensor products, which may be of independent interest.

基于在构造傅立叶代数上的最新进展的基础上，我们提供了局部紧致群的第一个示例，这些局部紧致群的傅立叶代数支持非零，交替2代同余；这是大型项目的第一步。尽管永远不可能完全限制这样的2乘代数，但傅立叶代数上的算子空间结构在我们的构造中起着至关重要的作用，相反的算子空间结构也是如此。

我们的构造有两个主要的技术要素：我们观察到[12]中的某些估计，它们作为从各个傅立叶代数到它们的对偶的映射“完全完全有界”。并且我们对某些算子空间张量产品建立了一个扭曲的包含结果，这可能是独立关注的。