论文标题
在傅立叶代数上构建交替的2个循环
Constructing alternating 2-cocycles on Fourier algebras
论文作者
论文摘要
我们基于在傅立叶代数上构建派生的最新进展的基础上，我们提供了本地紧凑型组的第一个例子，其傅立叶代数支持非零，交替的2个循环；这是大型项目的第一步。尽管这种2个循环永远无法完全界定，但是傅立叶代数上的操作员空间结构在我们的结构中起着至关重要的作用，相反的操作员空间结构也是如此。 我们的构建有两种主要的技术成分：我们观察到[H. H. Lee，J。Ludwig，E。Samei，N。Spronk，傅立叶代数的弱舒适性和抗Diagonal的局部合成，Adv。 Math。，292（2016）; ARXIV 1502.05214]屈服推导，它们是从各个傅立叶代数到其双重的地图“共完全界限”的；我们为某些操作员空间张量产品建立了扭曲的包含结果，这可能具有独立的兴趣。
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 [H. H. Lee, J. Ludwig, E. Samei, N. Spronk, Weak amenability of Fourier algebras and local synthesis of the anti-diagonal, Adv. Math., 292 (2016); arXiv 1502.05214] 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.
