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C*-代数的Murray-von Neumann分类理论的抽象架构
An Abstract Framework for Murray-von Neumann Type Classification Schemes of C*-algebras
Murray和von Neumann在对W*-代数进行分类工作时，主要的工具是刻画W*-代数中的投影的性质（事实上，W*-代数是由投影所生成的）.因为一般的C*-代数可能不包含任何非零的投影，所以不能将Murray和von Neumann的方法，直接地应用到C*-代数上来得出分类理论.本文作者在最近的两项工作中，分别使用C*-代数的开投影和正元来代替投影，得到两套平行的Murray-von Neumann式的分类理论.本文在简单描述了这两套分类理论之后，将会给出一个一般的分类架构，它可以用来得出好些C*-代数的分类理论（包括我们之前的两套理论），我们也会通过它来讨论各种分类理论之间的等价性，并给出之前两套理论的细化.
The famous work of Murray and von Neumann about decomposing W*-algebras into different types(which is known as the classification theory of W*-algebras) is based on the study of projections in W*-algebras.Different from W*-algebras(which are generated by projections), a C*-algebra may contain no non-zero projection.Therefore, we cannot transport the classification theory of Murray and von Neumann directly to C*-algebras.In our recent works, we have developed two classifying(or decomposition) schemes of C*-algebras using the properties of their open projections and properties of their positive elements, respectively.In this note, after a briefing of our two classifying schemes of C*-algebras, we introduce a more general classification framework that, on top of giving many other possible schemes, can be used to obtain, compare and refine the two classification schemes mentioned above.
C*-代数 / 开投影 / 正元 / Murray-von Neumann分类 {{custom_keyword}} /
C*-algebras / open projections / positive elements / Murray-von Neumann classification {{custom_keyword}} /
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