AI 中文总结
该研究将滨名内射包理论扩展到部分 C* - 动力系统领域，证明了系统与内射包理想交性质的关系，建立了系统内射包与其包络作用内射包间的联系，还表明对阿贝尔系统构造与相关函数代数一致，关键是考虑了广义系统概念。
AI 中文摘要
我们将滨名关于内射包的理论及其几个关键特性扩展到部分 C* - 动力系统领域。特别地，我们证明一个部分 C* - 动力系统具有理想交性质当且仅当其内射包具有该性质。我们论证中的一个关键要素是由单位 C* - 代数\(A\)在其内射包\(I(A)\)中的轨道生成的 C* - 代数所产生的一种新型单位化，它是对\(A\)上部分作用的单位化。对于任意已知有包络作用的单位部分 C* - 动力系统，我们建立了该系统的内射包与其包络作用的内射包之间的自然关系。对于阿贝尔部分 C* - 动力系统，我们表明我们的构造与相应变换群胚的弗斯滕伯格边界上的连续函数代数一致。在我们的工作中，考虑广义单位部分 C* - 动力系统的概念很关键，其中单位理想被单位遗传子代数所取代。
英文摘要
We extend Hamana's theory of injective envelopes, along with several key features of the theory, to the realm of partial C*-dynamical systems. In particular, we show that a partial C*-dynamical system has the ideal intersection property if and only if its injective envelope does. A key ingredient in our arguments is a new kind of unitization of a partial action on a unital C*-algebra $A$ arising from the C*-algebra generated by the orbits of $A$ in its injective envelope~$I(A)$. For an arbitrary unital partial C*-dynamical system, which is known to have an enveloping action, we establish a natural relationship between the injective envelope of the system and the injective envelope of its enveloping action. For an abelian partial C*-dynamical system, we show that our construction coincides with the algebra of continuous functions on the Furstenberg boundary of the corresponding transformation groupoid. It is crucial in our work to consider a notion of generalized unital partial C*-dynamical systems, in which the unital ideals are replaced by unital hereditary subalgebras.
