论文标题
伪群的等效性
Morita equivalence of pseudogroups
论文作者
论文摘要
我们利用伪群和逆数量框架之间的对应关系，以及最新的莫里塔对等量的描述，在双质二体基础上，逆量框架的相当性定义了伪群的莫里塔等效性，并调查了其应用。特别是，当且仅当它们相应的本地étalegroupoids所示时，两个假群是莫里塔等效的。我们探讨了我们对伪群的莫里塔等效性的定义与$ c^{\ ast} $ - 代数的强烈莫里塔等效性的常见概念与代数的常见概念，而这些概念导致了许多具体的结果。
We take advantage of the correspondence between pseudogroups and inverse quantal frames, and of the recent description of Morita equivalence for inverse quantal frames in terms of biprincipal bisheaves, to define Morita equivalence for pseudogroups and to investigate its applications. In particular, two pseudogroups are Morita equivalent if and only if their corresponding localic étale groupoids are. We explore the clear analogies between our definition of Morita equivalence for pseudogroups and the usual notion of strong Morita equivalence for $C^{\ast}$-algebras and these lead to a number of concrete results.
