泛C* 代数上的无穷和关系
Infinite sum relations on universal C*-algebras
摘要：
本文从生成元和关系出发，推广了一般的泛C* 代数理论，使某些关系可以用强算子拓扑来描述。特别地，我们可以允许一些无限和关系。我们证明了一个泛性质的代数，我们定义，我们展示了如何Cuntz代数的无限等距以及Exel-拉卡代数可以描述使用无限和关系。最后，我们给出了由投影和部分等距生成的C* 代数-代数是仅利用范数关系的泛C* 代数-代数的几个充分条件，以避免使用关于强算子拓扑的关系.
英文摘要：
We extend the usual theory of universal C*-algebras from generators and relations in order to allow some relations to be described using the strong operator topology. In particular, we can allow some infinite sum relations. We prove a universal property for the algebras we define and we show how the Cuntz algebra of infinite isometries as well as the Exel-Laca algebras can be described using infinite sum relations. Finally, we give some sufficient conditions for when a C*-algebra generated by projections and partial isometries is a universal C*-algebra using only norm relations, in case one still wants to avoid using relations with respect to the strong operator topology.
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