Continuous fields ofC*-algebras coming from group cocycles and actions
Continuous fields ofC*-algebras coming from group cocycles and actions
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来自群余循环和动作的 C* 代数的连续域
DOI：
10.1007/bf01442857
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发表时间：
1989
影响因子：
1.4
通讯作者：
M. Rieffel
中科院分区：
文献类型：
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作者：
M. Rieffel
最近，我一直在试图制定一个合适的C*-代数框架的主题变形量子化[-3，19]。C*-代数的连续域为这个框架提供了一个关键元素。到目前为止，我在这个C*-代数框架中构造的变形量子化的主要例子来自于让群上的上循环或群的作用变化。因此，有必要表明，人们以这种方式获得的C*-代数域确实是连续的。由于该材料具有通用性，并且在其他情况下也很有用[4-6、11-13]，因此在本文中对其进行单独阐述似乎是合适的。本文第1节回顾了已发表的连续领域的结果，我们将需要，以及讨论的事实，即我们将采取的方法涉及分别对待上半连续性和下半连续性。在第2节中，我们讨论了C*-代数的域的连续性，这些域是由群上的变化的上循环引起的，而在第3节中，我们对变化的作用也做了同样的讨论。
Recently I have been attempting to formulate a suitable C*-algebraic framework for the subject of deformation quantization [-3, 19]. Continuous fields of C*-algebras provide one of the key elements for this framework. The main examples of deformation quantizations which I have constructed up to now in this C*-algebra framework come from letting either cocycles on groups, or actions of groups, vary. It has thus become necessary to show that one obtains in this way fields of C*-aigebras that are indeed continuous. Since this material is of a general nature, and can be useful in other situations [4-6, 11-13] it has seemed appropriate to give a separate exposition of it, in the present article. Section 1 of this article contains a review of the published results on continuous fields which we will need, as well as a discussion of the fact that the approach which we will take involves treating upper and lower semi-continuity separately. In Sect. 2 we discuss the continuity of fields of C*-algebras which arise from varying cocycles on groups, while in Sect. 3 we do the same for actions which vary.