算子代数的非交换拓扑与局部结构
Non Commutative Topology and Local Structure of Operator Algebras
摘要：
本文从一个$W^{*}$-代数$M$出发，利用其（中心）投影对$M$进行裁剪得到的逆系统定义了$W^{*}$-代数的逆极限，并证明了这个原$W^{*}$-代数如何编码$M$的局部结构.对于$C^{*}$-代数，我们用它们的原子包络$W^{*}$-代数做同样的事情。我们调查的关系，这些想法的Akemann-Giles-Kummer非交换拓扑。最后我们用这些思想来研究Kac代数的局部结构。
英文摘要：
Starting with a $W^{*}$-algebra $M$ we use the inverse system obtained by cutting down $M$ by its (central) projections to define an inverse limit of $W^{*}$-algebras, and show that how this pro-$W^{*}$-algebra encodes the local structure of $M$. For the $C^{*}$-algebras we do the same thing using their atomic enveloping $W^{*}$-algebra . We investigate the relation of these ideas to the Akemann-Giles-Kummer non commutative topology. Finally we use these ideas to look at the local structure of Kac algebras.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
