03-496 Hellmut Baumg\"artel and Fernando Lled\'o

Duality of compact groups and Hilbert C*-systems for C*-algebras with a nontrivial center (155K, Latex2e) Nov 11, 03

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Abstract. 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. The abstract characterization of the mentioned Hilbert C*-system is expressed by means of an inclusion of C*-categories T_c < T, where T_c is 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_c and 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 an equivalence relation defined on the dual object of G. The chain group can be related to the character group of the center of G and determines the action of irreducible endomorphisms of A when restricted to Z. Moreover, C(G) encodes the possibility of defining a symmetry \epsilon also for the larger category T of the previous inclusion.

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