论文标题
基于伪造：伪预测的延伸属性和独特性
Aperiodicity: the almost extension property and uniqueness of pseudo-expectations
论文作者
论文摘要
我们证明了标题中的条件之间的意义，即在a c*-Algebra b中包含c*-Algebra a，并且我们还将其与其他几个属性联系起来，如果B是B群的交叉产品，用于群体，逆向半群或A。我们在A上的flose c*-Infienclusion a persection c*-crifusion aperiodic c*-Inclusion apection-excpect a strement pssepction-exccect。如果此外，如果独特的伪预测是忠实的，那么A在Cuntz预订的意义上支持B。几乎延伸的属性意味着临时性，如果b可分离，则匡威保持。当且仅当动作的双重类固定在拓扑上时，交叉产物的包含具有几乎扩展特性。拓扑上的无动作始终是至高无上的。如果A是可分离的或I型的，则拓扑结尾，多个和具有唯一的伪期望等效等效于A在所有中间C*-Algebras中检测理想的条件。另外，如果b是可分离的，那么所有这些条件都等同于几乎延伸属性。
We prove implications among the conditions in the title for an inclusion of a C*-algebra A in a C*-algebra B, and we also relate this to several other properties in case B is a crossed product for an action of a group, inverse semigroup or an étale groupoid on A. We show that an aperiodic C*-inclusion has a unique pseudo-expectation. If, in addition, the unique pseudo-expectation is faithful, then A supports B in the sense of the Cuntz preorder. The almost extension property implies aperiodicity, and the converse holds if B is separable. A crossed product inclusion has the almost extension property if and only if the dual groupoid of the action is topologically principal. Topologically free actions are always aperiodic. If A is separable or of Type I, then topological freeness, aperiodicity and having a unique pseudo-expectation are equivalent to the condition that A detects ideals in all intermediate C*-algebras. If, in addition, B is separable, then all these conditions are equivalent to the almost extension property.
