具有非平凡中心的C* 代数的紧群对偶与Hilbert C ~*-系
Duality of compact groups and Hilbert C*-systems for C*-algebras with a nontrivial center
摘要：
本文证明了当C ~*-代数A（对应的Hilbert C ~*-系统（F，G）的不动点代数）有非平凡中心Z且相对交换子满足极小条件A时，紧群的对偶理论.“\cap F = Z以及称为规则性的技术条件。本文用C*-范畴T_ \c < T的包含来表示Hilbert C*-系统的抽象特征，其中T_是A的自同态范畴的一个合适的DR-范畴，T是A的自同态范畴的满子范畴.这两个类别具有相同的对象，并且T的箭头可以从T_c的箭头和中心Z生成。在本分析中出现的一个重要新元素是阿贝尔群C（G），我们称之为G的链群，它可以由定义在G^（G的对偶对象）上的某些等价关系构造。同构于G的中心特征标群的链群决定了A的不可约自同态在限制于Z时的作用。此外，C（G）还对前面包含的更大范畴T定义对称性$ε$的可能性进行了编码。
英文摘要：
In the present paper we prove a duality theory for compact groups in the case when the C*-algebra A, the fixed point algebra of the corresponding Hilbert C*-system (F,G), has a nontrivial center Z and the relative commutant satisfies the minimality condition A.'\cap F = Z as well as a technical condition called regularity. The abstract characterization of the mentioned Hilbert C*-system is expressed by means of an inclusion of C*-categories T_\c < T, where T_cis a suitable DR-category and T a full subcategory of the category of endomorphisms of A. Both categories have the same objects and the arrows of T can be generated from the arrows of T_cand the center Z. A crucial new element that appears in the present analysis is an abelian group C(G), which we call the chain group of G, and that can be constructed from certain equivalence relation defined on G^, the dual object of G. The chain group, which is isomorphic to the character group of the center of G, determines the action of irreducible endomorphisms of A when restricted to Z. Moreover, C(G) encodes the possibility of defining a symmetry $ε$ also for the larger category T of the previous inclusion.
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