C* 代数上的可积和真作用及群的平方可积〔的〕表示
Integrable and proper actions on C*-algebras, and square-integrable representations of groups
摘要：
给出了C* 代数上局部紧群的{ \it真}作用的定义.我们证明了当C* 代数是交换的时，这个定义准确地捕捉了局部紧空间上的正常作用的通常概念。然后我们讨论如何定义{ \it广义不动点代数}。目的是证明广义不动点代数与交叉积代数中的理想是强Morita等价的，就像交换情形一样。证明了当C* 代数是交换的时，一个候选代数给出了所需的代数.但最近埃克塞尔已经表明，这个候选人是太大的一般。最后，我们详细考虑了这些想法的应用，以行动的一个局部紧群的代数紧算子（必然来自酉表示），并表明，这给了一个有吸引力的观点的主题平方可积〔的〕表示。
英文摘要：
We propose a definition of what should be meant by a {\it proper} action of a locally compact group on a C*-algebra. We show that when the C*-algebra is commutative this definition exactly captures the usual notion of a proper action on a locally compact space. We then discuss how one might define a {\it generalized fixed-point algebra}. The goal is to show that the generalized fixed-point algebra is strongly Morita equivalent to an ideal in the crossed product algebra, as happens in the commutative case. We show that one candidate gives the desired algebra when the C*-algebra is commutative. But very recently Exel has shown that this candidate is too big in general. Finally, we consider in detail the application of these ideas to actions of a locally compact group on the algebra of compact operators (necessarily coming from unitary representations), and show that this gives an attractive view of the subject of square-integrable representations.
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