An application of the DR-duality theory for compact groups to endomorphism categories of C*-algebras with nontrivial center

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dc.creatorBaumgaertel, Hellmut
dc.creatorLledo, Fernando
dc.date2000-12-06
dc.date.accessioned2026-07-07T04:39:04Z
dc.date.available2026-07-07T04:39:04Z
dc.descriptionIn Rev. Math. Phys. 4 (1997) 785 we study Hilbert-C* systems {F,G} where the fixed point algebra A has nontrivial center Z and where A'\cap F=Z is satisfied. The corresponding category of all canonical endomorphisms of A contains characteristic mutually isomorphic subcategories of the Doplicher/Roberts-type which are connected with the choice of distinguished G-invariant algebraic Hilbert spaces within the corresponding G-invariant Hilbert Z-modules. We present in this paper the solution of the corresponding inverse problem. More precisely, assuming that the given endomorphism category T of a C*-algebra A with center Z contains a certain subcategory of the DR-type, a Hilbert extension {F,G} of A is constructed such that T is isomorphic to the category of all canonical endomorphisms of A w.r.t. {F,G} and A'\cap F=Z. Furthermore, there is a natural equivalence relation between admissible subcategories and it is shown that two admissible subcategories yield A-module isomorphic Hilbert extensions iff they are equivalent. The essential step of the solution is the application of the standard DR-theory to the assigned subcategory.
dc.description10 pages, Latex2e
dc.identifierhttps://arxiv.org/abs/math/0012037
dc.identifierhttp://arxiv.org/abs/math/0012037
dc.identifierFields Inst.Commun. 30 (2001) 1-10
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60514
dc.subjectOperator Algebras
dc.subjectMathematical Physics
dc.subject47L65;22D25;46L08
dc.titleAn application of the DR-duality theory for compact groups to endomorphism categories of C*-algebras with nontrivial center
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