论文标题
在原始理想空间上粘合希尔伯特C*模型
Gluing Hilbert C*-modules over the primitive ideal space
论文作者
论文摘要
我们表明，雷伯恩（Raeburn）在对PICARD组的计算中引入的Hilbert模块的粘合结构，可以通过使用Haagerup Tensor产品的代数参数将任意C*-Elgebras应用于任意C*-Elgebras。我们通过识别C* - 代数上的Hilbert模块的胶合数据类别的类别，将此结果置于下降理论的背景下，其中具有C*-Coalgebras上的综合类别，从而从代数几何形状提供了标准结构的Hilbert-Module版本。结果，我们表明，如果两个C* - 代数具有相同的原始理想空间t，并且是莫里塔等于t的莫里塔，则相对于t，其PICARD组相对于t是同构的。
We show that the gluing construction for Hilbert modules introduced by Raeburn in his computation of the Picard group of a continuous-trace C*-algebra (Trans. Amer. Math. Soc., 1981) can be applied to arbitrary C*-algebras, via an algebraic argument with the Haagerup tensor product. We put this result into the context of descent theory by identifying categories of gluing data for Hilbert modules over C*-algebras with categories of comodules over C*-coalgebras, giving a Hilbert-module version of a standard construction from algebraic geometry. As a consequence we show that if two C*-algebras have the same primitive ideal space T, and are Morita equivalent up to a 2-cocycle on T, then their Picard groups relative to T are isomorphic.
