利用Hilbert右C*-模的群的射影表示
Projective representations of groups using Hilbert right C*-modules
摘要：
群的射影表示是在1904年由Issai Schur提出的。它通过一个扭曲因子而不同于群的正常表示。它从群T和T^2上的标量值函数f开始，满足条件：f（1，1）=1，|f（s，t）|=1，且f（r，s）f（rs，t）=f（r，st）f（s，t）. T被f扭曲的射影表示是希尔伯特空间l ^2（T）上C*-算子代数的一个有单位元的C *-子代数。这个表示可以用来构造C* 代数的许多例子。通过用任意的单位C* 代数-代数（作为f的值域）代替标量，从本质上增强了它的应用范围.本文给出的群的射影表示与离散群的向量积的构造有相似之处。它为创造许多K理论开辟了道路。在第一节中，我们介绍了一些结果，这是需要为这个建设，这是在第二节中开发。在第三节中，我们给出了用这种方法得到的C* 代数的一些例子。最后一节给出了一类特殊代数（Clifford代数）的例子。
英文摘要：
The projective representation of groups was introduced in 1904 by Issai Schur. It differs from the normal representation of groups by a twisting factor. It starts with a group T and a scalar valued function f on T^2 satisfying the conditions: f(1,1)=1, |f(s,t)|=1, and f(r,s)f(rs,t)=f(r,st)f(s,t) for all r,s,t in T. The projective representation of T twisted by f is a unital C*-subalgebra of the C*-algebra of operators on the Hilbert space l^2(T). This representation can be used in order to construct many examples of C*-algebras. By replacing the scalars with an arbitrary unital C*-algebra (as range of f) the field of applications is enhanced in an essential way. The projective representation of groups, which we present in this paper, has some similarities with the construction of cross products with discrete groups. It opens the way to create many K-theories. In a first section we introduce some results which are needed for this construction, which is developed in the second section. In a third section we present some examples of C*-algebras obtained by this method. Examples of a special kind (the Clifford algebras) are presented in the last section.
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